November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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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:
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