USU Math 4610
Author: Philip Nelson
The Kronecker product is an operation on two matrices of arbitrary size resulting in a block matrix. It is a generalization of the outer product from vectors to matrices, and gives the matrix of the tensor product with respect to a standard choice of basis [1].
The Kronecker Product is used in solving Sylvester and Lupunov equations which is a system of the form \(AX + XB = C\) where \(A\in R^{nxn},B\in R^{mxm},C\in R^{nxm}\). These systems arise naturally in stability theory [2].
Another application of the Kronecker product arises in defining the search directions for primal-dual interior-point methods in semidefinite programming [3].
Last Modified: October 2018