Kronecker Product

In mathematics, the Kronecker product, denoted by , is an operation on two matrices of arbitrary size resulting in a block matrix. It is a special case of a tensor product. The Kronecker product should not be confused with the usual matrix multiplication, which is an entirely different operation. It is named after German mathematician Leopold Kronecker.
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The Kronecker (direct) product of 2 matrices A, with p rows and q columns, and B, with m rows and n columns, is the matrix with pm rows and qn columns given by
= aij B
For example, if

and

then

Kronecker Product matrices have a number of useful properties (for a summary of these properties, see Hocking, 1985).