Are there any nice ways of encoding tensor products of matrices using index notation? I.e. for standard matrix multiplication we have
$$(AB)_{ij} = \sum_k A_{ik} B_{kj} $$
Is there anything similar for tensor products?
$$(A\otimes B)_{ij} = ???$$
Tensor Product Between Matrices Index Notation
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1 Answers
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If by "tensor product" you mean the Kronecker product, then we can write in block-matrix notation $$ (A \otimes B) = [a_{ij}B]_{i,j = 1}^n $$ Another thing you can say is that if $B$ is $m \times n$, then $$ (A \otimes B)_{(i-1)m + p,(j-1)n + q} = a_{ij}b_{pq} $$