It is well-known that a Sylvester Hadamard matrix can be described by means of a cocycle. In this paper it is shown that the additional internal structure in a Sylvester Hadamard matrix, provided by the cocycle, is su cient to guarantee some kind of reduction in the computational complexity of calculating its permanent using Ryser's formula. A Hadamard matrix H of order n is an n× n matrix with...

A matrix is called a multiple resultant matrix associated to two matrix polynomials when it becomes singular if and only if the two matrix polynomials have at least one common eigenvalue. In this paper a new multiple resultant matrix is introduced. It concerns the Fisher information matrix (FIM) of a stationary vector autoregressive and moving average time series process (VARMA). The two matrix...

Some complex quaternionic equations in the type AX - XB = C are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained.

We prove Roth-type theorems for systems of matrix equations including an arbitrary mix of Sylvester and ⋆-Sylvester equations, in which the transpose or conjugate transpose of the unknown matrices also appear. In full generality, we derive consistency conditions by proving that such a system has a solution if and only if the associated set of 2× 2 block matrix representations of the equations a...

LOW-RANK SOLUTION METHODS FOR LARGE-SCALE LINEAR MATRIX EQUATIONS Stephen D. Shank DOCTOR OF PHILOSOPHY Temple University, May, 2014 Professor Daniel B. Szyld, Chair We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on standard, extended and rational Krylov subspaces to solve equations w...

We consider the uniqueness of solution (nonsingularity) of systems of r generalized Sylvester and ⋆-Sylvester equations with n × n coefficient matrices. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ⋆-Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix penc...