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 generalization of the outer product (which is denoted by the same symbol) from vectors to matrices, and gives the matrix of the tensor product with respect to a standard choice of basis. The Kronecker product should not be confused with the usual matrix multiplication, which is an entirely different operation.
The Kronecker product is named after Leopold Kronecker, even though there is little evidence that he was the first to define and use it. Indeed, in the past the Kronecker product was sometimes called the Zehfuss matrix, after Johann Georg Zehfuss who in 1858 described the matrix operation we now know as the Kronecker product.
If A is an m × n matrix and B is a p × q matrix, then the Kronecker product A ⊗ B is the mp × nq block matrix:
more explicitly:
More compactly, we have
...
Wikipedia