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Tags

#calculus #mathematics #tensors #vectors

Question

So in 3-dimensional space, a second-rank tensor is represented by 3^{2} = 9 numbers. In N-dimensional space, [how many numbers for scalar, vector and tensor?]

Answer

scalars still require only one number, vectors require N numbers, and tensors require N^{R} numbers

Tags

#calculus #mathematics #tensors #vectors

Question

So in 3-dimensional space, a second-rank tensor is represented by 3^{2} = 9 numbers. In N-dimensional space, [how many numbers for scalar, vector and tensor?]

Answer

?

Tags

#calculus #mathematics #tensors #vectors

Question

So in 3-dimensional space, a second-rank tensor is represented by 3^{2} = 9 numbers. In N-dimensional space, [how many numbers for scalar, vector and tensor?]

Answer

scalars still require only one number, vectors require N numbers, and tensors require N^{R} numbers

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#### Parent (intermediate) annotation

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So in 3-dimensional space, a second-rank tensor is represented by 3 2 = 9 numbers. In N-dimensional space, scalars still require only one number, vectors require N numbers, and tensors require N R numbers

#### Original toplevel document (pdf)

owner: shihabdider - (no access) - A Student's Guide to Vectors and Tensors, p15

So in 3-dimensional space, a second-rank tensor is represented by 3 2 = 9 numbers. In N-dimensional space, scalars still require only one number, vectors require N numbers, and tensors require N R numbers

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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