- #1
KFC
- 488
- 4
Hi there,
I have a question about tensor rank. As we know, zero-rank tensor is scalar, rank one tensor is a vector and rank two tensor is a 3x3 matrix. Moreover, scalar and vector can also be written in the form of matrix. However, for higher rank tensor, says rank 4, according to the definition, there are 3^4 = 81 entries. And many textbook wrote rank 4 tensor, in index form, as
[tex]T_{\alpha, \beta, \gamma, \delta}[/tex]
i.e., there are four indices. So can we also write higher rank tensor (rank 4 or above) with a square matrix? If so, what does each index mean?
I have a question about tensor rank. As we know, zero-rank tensor is scalar, rank one tensor is a vector and rank two tensor is a 3x3 matrix. Moreover, scalar and vector can also be written in the form of matrix. However, for higher rank tensor, says rank 4, according to the definition, there are 3^4 = 81 entries. And many textbook wrote rank 4 tensor, in index form, as
[tex]T_{\alpha, \beta, \gamma, \delta}[/tex]
i.e., there are four indices. So can we also write higher rank tensor (rank 4 or above) with a square matrix? If so, what does each index mean?