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Given two symmetric matrices, $A \in \mathbb{R}^{n \times n}$ and $B \in \mathbb{R}^{m \times m}$, is there any property of the Kronecker product which relates to matrix multiplication?

More specifically, what is $(A \otimes B)C$? And what should the dimensions of $C$ be?

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1 Answer

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In general there is no nice formula for $(A\otimes B)C$. However, if you know $C=U\otimes V$, then $$ (A\otimes B)(U\otimes V) = (AU)\otimes (BV). $$ SeeKronecker product.

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