TITLE: Kronecker Product and matrix multiplication property
QUESTION [5 upvotes]: 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, $(A \otimes B)C = $? 
And what should be the dimensions of C? 
Thanks in advance

REPLY [6 votes]: 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.