G.6 KRONECKER AND SCHUR PRODUCTS
Definition: Kronecker Product The Kronecker product of matrices and is a size block matrix:
(G.50)
where the upper-left block is
(G.51)
and likewise for the other blocks.
Although the Kronecker product is associative, it is not commutative: . Note also that A and B can be vectors: if is a column vector and is a row vector, then is a matrix. For this case, the Kronecker product reduces to the standard vector outer product abT.
Definition: Schur Product For matrices and , the Schur product is obtained by a multiplication of their entries element-wise:
Get Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.