Kronecker Product of Matrices and Applications to Two-Point Boundary Value problems associated with first order Matrix Difference Systems

This paper presents a criteria for the existence and uniqueness of solutions to two-point boundary value problems associated with a system of Kronecker product first order differential equation. Some of the natural questions on Kronecker product of matrices about seemingly “simple” cases are still unanswered in spite of their increasing interest and hence some significant results on Kronecker product of matrices are answered in this paper. We mainly explain a set of necessary and sufficient conditions on the decomposition of a matrix into Kronecker product of two matrices.