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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?

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# Tensor and matrices

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