In this paper, existence and uniqueness of solutions to two-point boundary value problem associated with the non-linear kronecker product Lyapunov system on time scales are derived. These generalize the results obtained for two-point boundary value problems involving kronecker products. Bartles-Stewart algorithm and a modified QR-algorithm are presented for solving the system of equations invol...

This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vecpermutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of...

Recursive constructions are given which permit, under conditions described in the paper, a (v, b, r, k, lambda)configuration to be used to obtain a (v', b', r', k, lambda)-configuration. Although there are many equivalent definitions we will mean by a (v, b, r, k, lambda)-configuration or BIBD that (0, 1)-matrix A of size v x b with row sum r and column sum k satisfying AAT = (r lambda)I + lamb...

We present new proofs and generalizations of unimodality of the q-binomial coefficients ( n k ) q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker coefficients of representations of Sn. Other applications of this approach include strict unimodality of the diagonal q-binomial coefficients and unimodality of certa...

An invertible matrix is called a Perron similarity if one of its columns and the corresponding row inverse are both nonnegative or nonpositive. Such matrices relevance import in study eigenvalue problem. In this work, Kronecker products similarities examined used to construct ideal all whose rows extremal.

The Khatri-Rao and Tracy-Singh products for partitioned matrices are viewed as generalized Hadamard and generalized Kronecker products, respectively. We define the KhatriRao and Tracy-Singh sums for partitioned matrices as generalized Hadamard and generalized Kronecker sums and derive some results including matrix equalities and inequalities involving the two sums. Based on the connection betwe...