Now we are ready to give the formal definition of a vector space. A vector space is a set V along with an addition on V and a scalar multiplication on V such that the following properties hold:
[...]
Answer
commutativity
u + v = v + u for all u, v ∈ V;
associativity
(u+v)+w = u+(v +w) and (ab)v = a(bv) for all u,v,w ∈ V and all a,b ∈ F;
additive identity
there exists an element 0 ∈ V such that v +0 = v for all v ∈ V;
additive inverse
for every v ∈ V, there exists w ∈ V such that v + w = 0;
multiplicative identity
1v = v for all v ∈ V;
distributive properties
a(u +v) = au +av and (a +b)u = au +bu for all a,b ∈ F and all u,v ∈ V.
Question
Now we are ready to give the formal definition of a vector space. A vector space is a set V along with an addition on V and a scalar multiplication on V such that the following properties hold:
[...]
Answer
?
Question
Now we are ready to give the formal definition of a vector space. A vector space is a set V along with an addition on V and a scalar multiplication on V such that the following properties hold:
[...]
Answer
commutativity
u + v = v + u for all u, v ∈ V;
associativity
(u+v)+w = u+(v +w) and (ab)v = a(bv) for all u,v,w ∈ V and all a,b ∈ F;
additive identity
there exists an element 0 ∈ V such that v +0 = v for all v ∈ V;
additive inverse
for every v ∈ V, there exists w ∈ V such that v + w = 0;
multiplicative identity
1v = v for all v ∈ V;
distributive properties
a(u +v) = au +av and (a +b)u = au +bu for all a,b ∈ F and all u,v ∈ V.
If you want to change selection, open original toplevel document below and click on "Move attachment"
Parent (intermediate) annotation
Open it Now we are ready to give the formal definition of a vector space. A vector space is a set V along with an addition on V and a scalar multiplication on V such that the following properties hold:
commutativity
u + v = v + u for all u, v ∈ V;
associativity
(u+v)+w = u+(v +w) and (ab)v = a(bv) for all u,v,w ∈ V and all a,b ∈ F;
additive identity
there exists an element 0 ∈ V such that v +0 = v for all v ∈ V;
additive inverse
for every v ∈ V, there exists w ∈ V such that v + w = 0;
multiplicative identity
1v = v for all v ∈ V;
distributive properties
a(u +v) = au +av and (a +b)u = au +bu for all a,b ∈ F and all u,v ∈ V.
Original toplevel document (pdf)
owner: eshi - (no access) - Sheldon_Axler_Linear_Algebra_Done_Right.pdf, p23
Summary
status
not learned
measured difficulty
37% [default]
last interval [days]
repetition number in this series
0
memorised on
scheduled repetition
scheduled repetition interval
last repetition or drill
Details
No repetitions
Discussion
Do you want to join discussion? Click here to log in or create user.