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If $A$ is an $m \times n$ matrix and $B$ is a $p \times q$ matrix, then the Kronecker product $C = A \otimes B$ is an $mp \times nq$ matrix. Assume that I have a matrix $C$ and that I want to find the matrices $A$ and $B$ such that $C=A\otimes B$, how can I find them?

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Firstly, they aren't uniquely determined, consider $C=[0]_{m,n}$ and any $m$ by $n$ matrix $A$, then we have $$A\otimes [0]_{1,1}=C.$$

If you want to recover some $A,B$ such that $A\otimes B = C$, then you can take $C=C\otimes [1]$ (meaning the identity matrix in $M_1(R)$).

  • I assume that for the OP the sizes of the matrices are fixed. – Qiaochu Yuan Sep 12 '20 at 19:18
  • If A is an m×n matrix and B is a p×q matrix, then the Kronecker product C=A⊗B is an mp×nq matrix. Assume that I have a matrix C and matrix A too such that I want to find the initial matrix B how can I find that? – Tehreem zia Sep 12 '20 at 20:41