On the Kronecker Product of Matrices and Their Applications To Linear Systems Via Modified QR-Algorithm

This paper studies and supplements the proofs of the properties of the Kronecker Product of two matrices of different orders. We observe the relation between the singular value decomposition of the matrices and their Kronecker product and the relationship between the determinant, the trace, the rank and the polynomial matrix of the Kronecker products.  We also establish the best least square solutions of the Kronecker product system of equations by using modified QR-algorithm.