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#### Annotation 1731573714188

 #sprectral-theorem #stochastics Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem[1][2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval.

Karhunen–Loève theorem - Wikipedia
Karhunen–Loève theorem - Wikipedia Karhunen–Loève theorem From Wikipedia, the free encyclopedia (Redirected from Karhunen–Loeve expansion) Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem [1] [2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation is also known as Hotelling Transform and Eigenvector Transform, and is closely related to Principal Component Analysis (PCA) technique widely used in image processing

#### Annotation 1732138896652

 #spanish Él seguía deprimido, aunque dijo que había dormido bien.

#### Flashcard 1732485451020

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#sprectral-theorem #stochastics
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the Karhunen–Loève theorem represents [...] as an infinite linear combination of orthogonal functions

a stochastic process

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d> Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem [1] [2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. <html>

#### Original toplevel document

Karhunen–Loève theorem - Wikipedia
Karhunen–Loève theorem - Wikipedia Karhunen–Loève theorem From Wikipedia, the free encyclopedia (Redirected from Karhunen–Loeve expansion) Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem [1] [2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation is also known as Hotelling Transform and Eigenvector Transform, and is closely related to Principal Component Analysis (PCA) technique widely used in image processing

#### Flashcard 1732487023884

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#sprectral-theorem #stochastics
Question

the Karhunen–Loève theorem represents a stochastic process as [...]

an infinite linear combination of orthogonal functions

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p to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem [1] [2] is a representation of a stochastic process as <span>an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. <span><body><html>

#### Original toplevel document

Karhunen–Loève theorem - Wikipedia
Karhunen–Loève theorem - Wikipedia Karhunen–Loève theorem From Wikipedia, the free encyclopedia (Redirected from Karhunen–Loeve expansion) Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem [1] [2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation is also known as Hotelling Transform and Eigenvector Transform, and is closely related to Principal Component Analysis (PCA) technique widely used in image processing

#### Annotation 1738457615628

 #spanish Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato.

Mourinho: Alexis no llegó al Manchester United por dinero
Te gustan las de arriba. "Esas son muy agradables, tan naranjas, tan redondas, tan llenas de jugo, pero no puedes llegar allí, así que dices: 'No quiero ir allí' o 'No me gustaron, prefiero las otras'. ' Me recuerda esa historia ". <span>Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato. Al final, United no pagó una tarifa después de aceptar y permitir que Mkhitaryan se mude al Emirates. Sánchez ha firmado un contrato de cuatro años y medio en Old Trafford por valor de

#### Annotation 1738459712780

 #spanish Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia.

Mourinho: Alexis no llegó al Manchester United por dinero
ciones. Decidió venir aquí y tienes que preguntarle por qué". Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. <span>Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia. Agregó: "Creo que Alexis me recuerda un poco de la historia, no sé, no es una historia, casi una metáfora, cuando ves el árbol con naranjas increíbles en la parte superior del árbo

#### Annotation 1738461285644

 #spanish Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes.

Mourinho: Alexis no llegó al Manchester United por dinero
ó más dinero que nosotros, creo que incluso Everton gastó más dinero que nosotros. No creo que ese sea el problema. "No sé. Alexis podía ir a todas partes. Tenía muchas opciones. Decidió venir aquí y tienes que preguntarle por qué". <span>Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratar

#### Annotation 1738462858508

 #spanish Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos.

Mourinho: Alexis no llegó al Manchester United por dinero
el Manchester United sobre Manchester City no estuvo motivada por el dinero. United y City se enfrentaron cara a cara por el chileno este mes con el delantero moviéndose a Old Trafford y Henrikh Mkhitaryan firmando por el Arsenal a cambio. <span>Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos. Lleva ESPN a todos lados Si quieres recibir alertas del Futbol Europeo, descarga la App ahora. espn.com/app » Él dijo en una conferencia de prensa el jueves: "Sé que si otros club

#### Annotation 1738464431372

 #spanish Jose Mourinho: Alexis Sánchez no se mudó al Manchester United por dinero

Mourinho: Alexis no llegó al Manchester United por dinero
stos colores" 5hESPN Digital La Copa del Rey se tiñe de azulgrana 5hJordi Blanco | ESPN Digital Jugadores que militan en Europa tienen pie y medio en el Mundial 5hIván Cañada América cierra pase de Romero a Independiente 6hRicardo Cariño <span>Jose Mourinho: Alexis Sánchez no se mudó al Manchester United por dinero El jugador chileno firmó contrato con el Manchester United el lunes. Manchester United/Man Utd via Getty Images Facebook Twitter Facebook Messenger Correo-e Comentar 9:20 AM CT Rob Daw

#### Flashcard 1738467314956

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#spanish
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Jose Mourinho: Alexis Sánchez no [...] al Manchester United por dinero
se mudó

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Jose Mourinho: Alexis Sánchez no se mudó al Manchester United por dinero

#### Original toplevel document

Mourinho: Alexis no llegó al Manchester United por dinero
stos colores" 5hESPN Digital La Copa del Rey se tiñe de azulgrana 5hJordi Blanco | ESPN Digital Jugadores que militan en Europa tienen pie y medio en el Mundial 5hIván Cañada América cierra pase de Romero a Independiente 6hRicardo Cariño <span>Jose Mourinho: Alexis Sánchez no se mudó al Manchester United por dinero El jugador chileno firmó contrato con el Manchester United el lunes. Manchester United/Man Utd via Getty Images Facebook Twitter Facebook Messenger Correo-e Comentar 9:20 AM CT Rob Daw

#### Flashcard 1738468887820

Tags
#spanish
Question
Se informó que City [...] de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez.
se retiró

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Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos. </

#### Original toplevel document

Mourinho: Alexis no llegó al Manchester United por dinero
el Manchester United sobre Manchester City no estuvo motivada por el dinero. United y City se enfrentaron cara a cara por el chileno este mes con el delantero moviéndose a Old Trafford y Henrikh Mkhitaryan firmando por el Arsenal a cambio. <span>Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos. Lleva ESPN a todos lados Si quieres recibir alertas del Futbol Europeo, descarga la App ahora. espn.com/app » Él dijo en una conferencia de prensa el jueves: "Sé que si otros club

#### Flashcard 1738470460684

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#spanish
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Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha [...] los reclamos.

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Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos.

#### Original toplevel document

Mourinho: Alexis no llegó al Manchester United por dinero
el Manchester United sobre Manchester City no estuvo motivada por el dinero. United y City se enfrentaron cara a cara por el chileno este mes con el delantero moviéndose a Old Trafford y Henrikh Mkhitaryan firmando por el Arsenal a cambio. <span>Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos. Lleva ESPN a todos lados Si quieres recibir alertas del Futbol Europeo, descarga la App ahora. espn.com/app » Él dijo en una conferencia de prensa el jueves: "Sé que si otros club

#### Flashcard 1738472033548

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#spanish
Question
Sánchez [...] su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes.
selló

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Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. <

#### Original toplevel document

Mourinho: Alexis no llegó al Manchester United por dinero
ó más dinero que nosotros, creo que incluso Everton gastó más dinero que nosotros. No creo que ese sea el problema. "No sé. Alexis podía ir a todas partes. Tenía muchas opciones. Decidió venir aquí y tienes que preguntarle por qué". <span>Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratar

#### Flashcard 1738473606412

Tags
#spanish
Question
Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho [...] que podría tratarse de pura envidia.
sugirió

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Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia.

#### Original toplevel document

Mourinho: Alexis no llegó al Manchester United por dinero
ciones. Decidió venir aquí y tienes que preguntarle por qué". Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. <span>Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia. Agregó: "Creo que Alexis me recuerda un poco de la historia, no sé, no es una historia, casi una metáfora, cuando ves el árbol con naranjas increíbles en la parte superior del árbo

#### Flashcard 1738475179276

Tags
#spanish
Question
Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura [...].
envidia

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><head> Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia. <html>

#### Original toplevel document

Mourinho: Alexis no llegó al Manchester United por dinero
ciones. Decidió venir aquí y tienes que preguntarle por qué". Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. <span>Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia. Agregó: "Creo que Alexis me recuerda un poco de la historia, no sé, no es una historia, casi una metáfora, cuando ves el árbol con naranjas increíbles en la parte superior del árbo

#### Flashcard 1738476752140

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#spanish
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Las fuentes le han dicho a ESPN FC que Arsenal [...] inicialmente en 49.5 millones de dólares por Sánchez
cotizaba

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Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato

#### Original toplevel document

Mourinho: Alexis no llegó al Manchester United por dinero
Te gustan las de arriba. "Esas son muy agradables, tan naranjas, tan redondas, tan llenas de jugo, pero no puedes llegar allí, así que dices: 'No quiero ir allí' o 'No me gustaron, prefiero las otras'. ' Me recuerda esa historia ". <span>Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato. Al final, United no pagó una tarifa después de aceptar y permitir que Mkhitaryan se mude al Emirates. Sánchez ha firmado un contrato de cuatro años y medio en Old Trafford por valor de

#### Flashcard 1738479635724

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#spanish
Question
Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, [...] que el delantero tiene solo seis meses restantes en su contrato.
a pesar de

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Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato.

#### Original toplevel document

Mourinho: Alexis no llegó al Manchester United por dinero
Te gustan las de arriba. "Esas son muy agradables, tan naranjas, tan redondas, tan llenas de jugo, pero no puedes llegar allí, así que dices: 'No quiero ir allí' o 'No me gustaron, prefiero las otras'. ' Me recuerda esa historia ". <span>Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato. Al final, United no pagó una tarifa después de aceptar y permitir que Mkhitaryan se mude al Emirates. Sánchez ha firmado un contrato de cuatro años y medio en Old Trafford por valor de

#### Flashcard 1738586590476

Tags
#measure-theory #stochastics
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Radon, Fréchet, and others generalized the new real analysis to [...of...on...]
integrals of real-valued functions on arbitrary spaces

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What Kolmogorov did was to say that the new real analysis that had started with the PhD thesis of Henri Lebesgue (1902) and had been rapidly generalized to integrals of real-valued functions on arbitrary spaces by Radon, Fr´echet, and others (called Lebesgue integration or abstract integration) should also be used in probability theory

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#### Annotation 1741788941580

 #linear-algebra In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R3) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane containing them.

Cross product - Wikipedia
edia, the free encyclopedia Jump to: navigation, search This article is about the cross product of two vectors in three-dimensional Euclidean space. For other uses, see Cross product (disambiguation). <span>In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product). If two vectors have the same

#### Annotation 1743950581004

 #state-space-models Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields.

Belief propagation - Wikipedia
st of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2009) (Learn how and when to remove this template message) <span>Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node, conditional on any observed nodes. Belief propagation is commonly used in artificial intelligence and information theor

#### Flashcard 1743952678156

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#state-space-models
Question
[...] is also known as sum-product message passing
Belief propagation

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Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. </sp

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Belief propagation - Wikipedia
st of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2009) (Learn how and when to remove this template message) <span>Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node, conditional on any observed nodes. Belief propagation is commonly used in artificial intelligence and information theor

#### Flashcard 1744130936076

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#state-space-models
Question
Belief propagation is also known as [...]
sum-product message passing

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Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields.

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Belief propagation - Wikipedia
st of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2009) (Learn how and when to remove this template message) <span>Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node, conditional on any observed nodes. Belief propagation is commonly used in artificial intelligence and information theor

#### Flashcard 1744254930188

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#linear-algebra
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the cross product is [...123...].

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In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane

#### Original toplevel document

Cross product - Wikipedia
edia, the free encyclopedia Jump to: navigation, search This article is about the cross product of two vectors in three-dimensional Euclidean space. For other uses, see Cross product (disambiguation). <span>In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product). If two vectors have the same

#### Flashcard 1744257289484

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#linear-algebra
Question
the cross product is occasionally called directed area product to emphasize [...]
the geometric significance

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In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a ve

#### Original toplevel document

Cross product - Wikipedia
edia, the free encyclopedia Jump to: navigation, search This article is about the cross product of two vectors in three-dimensional Euclidean space. For other uses, see Cross product (disambiguation). <span>In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product). If two vectors have the same

#### Flashcard 1749112720652

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#hilbert-space
Question
Hilbert spaces are [...]: there are enough limits in the space to allow the techniques of calculus to be used.
complete

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Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used.

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Hilbert space - Wikipedia
e state of a vibrating string can be modeled as a point in a Hilbert space. The decomposition of a vibrating string into its vibrations in distinct overtones is given by the projection of the point onto the coordinate axes in the space. <span>The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces. The earliest Hilbert spaces were studied from this point o

#### Flashcard 1753209769228

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#vector-space
Question
a norm is a function that assigns a [...] to each vector in a vector space
nonnegative length or size

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a norm is a function that assigns a strictly positive length or size to each vector (bar zero vector) in a vector space

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Norm (mathematics) - Wikipedia
analysis. For field theory, see Field norm. For ideals, see Ideal norm. For group theory, see Norm (group). For norms in descriptive set theory, see prewellordering. In linear algebra, functional analysis, and related areas of mathematics, <span>a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

#### Flashcard 1756885028108

Tags
#Karush-Kuhn-Tucker-condition #has-images
[unknown IMAGE 1756483423500]
Question
the function f(x) will only be at a maximum if λ satisfies [...formula...]
$$\lambda > 0$$

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In optimization with inequality constraint, the sign of the Lagrange multiplier is crucial, because the function f(x) will only be at a maximum if its gradient is oriented away from the region g(x) > 0

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#### Annotation 1758542826764

 [unknown IMAGE 1758545186060] #has-images #sets In mathematics, the infimum of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

Infimum and supremum - Wikipedia
ed sets the infimum and the minimum are equal. [imagelink] A set A of real numbers (blue balls), a set of upper bounds of A (red diamond and balls), and the smallest such upper bound, that is, the supremum of A (red diamond). <span>In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists. Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used. The supremum (abbreviated sup; plural suprema) of a subset S of a partially ordered set T is th

#### Flashcard 1758547283212

Tags
#has-images #sets
[unknown IMAGE 1758545186060]
Question
the infimum of a subset S of a partially ordered set T is [...], if such an element exists.
the greatest element in T that is less than or equal to all elements of S

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In mathematics, the infimum of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

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Infimum and supremum - Wikipedia
ed sets the infimum and the minimum are equal. [imagelink] A set A of real numbers (blue balls), a set of upper bounds of A (red diamond and balls), and the smallest such upper bound, that is, the supremum of A (red diamond). <span>In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists. Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used. The supremum (abbreviated sup; plural suprema) of a subset S of a partially ordered set T is th

#### Flashcard 1758548856076

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#has-images #sets
[unknown IMAGE 1758545186060]
Question
[...] is the greatest element in T that is less than or equal to all elements of S, if such an element exists.
the infimum of a subset S of a partially ordered set T

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In mathematics, the infimum of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

#### Original toplevel document

Infimum and supremum - Wikipedia
ed sets the infimum and the minimum are equal. [imagelink] A set A of real numbers (blue balls), a set of upper bounds of A (red diamond and balls), and the smallest such upper bound, that is, the supremum of A (red diamond). <span>In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists. Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used. The supremum (abbreviated sup; plural suprema) of a subset S of a partially ordered set T is th

#### Flashcard 1759054269708

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#linear-algebra
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the cross product is occasionally called [...] to emphasize the geometric significance
directed area product

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In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a ve

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Cross product - Wikipedia
edia, the free encyclopedia Jump to: navigation, search This article is about the cross product of two vectors in three-dimensional Euclidean space. For other uses, see Cross product (disambiguation). <span>In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product). If two vectors have the same

#### Flashcard 1759663230220

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#lebesgue-space
Question
Lp spaces are function spaces defined using a natural generalization of [...]
the p-norm for finite-dimensional vector spaces.

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In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.

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Lp space - Wikipedia
Lp space - Wikipedia L p space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). L p

#### Annotation 1760853101836

 #calculus Calculation of the total derivative of with respect to assumes that the other arguments too depend on t.

Total derivative - Wikipedia
effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). <span>Calculation of the total derivative of f {\displaystyle f} with respect to t {\displaystyle t} does not assume that the other arguments are constant while t {\displaystyle t} varies; instead, it assumes that the other arguments too depend on t {\displaystyle t} . The total derivative includes these indirect dependencies to find the overall dependency of f {\displaystyle f} on t

#### Annotation 1760855198988

 #calculus The total derivative of a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.

Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the

#### Flashcard 1760858606860

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#calculus
Question
The total derivative is the [...description...]
limiting ratio of ∆ƒ/∆t

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The total derivative of a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.

#### Original toplevel document

Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the

#### Flashcard 1760860179724

Tags
#calculus
Question
The total derivative taking into account the exogenous argument's [...] to the function
direct and indirect effects

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a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's <span>direct effect as well as indirect effects via the other arguments of the function. <span><body><html>

#### Original toplevel document

Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the

#### Flashcard 1760861752588

Tags
#calculus
Question
The [...] of a function of several variables, e.g., , , , with respect to an exogenous argument is defined as
total derivative

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The total derivative of a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous ar

#### Original toplevel document

Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the

#### Flashcard 1760864111884

Tags
#calculus
Question
Calculation of the total derivative of with respect to assumes that [...].