Canonical systems and transfer matrix-functions

Generalized matrix functions, determinant and permanent

In this paper, using permutation matrices or symmetric matrices, necessary and sufficient conditions are given for a generalized matrix function to be the determinant or the permanent. We prove that a generalized matrix function is the determinant or the permanent if and only if it preserves the product of symmetric permutation matrices. Also we show that a generalized matrix function is the de...

Lommel Matrix Functions

The main objective of this work is to develop a pair of Lommel matrix functions suggested by the hypergeometric matrix functions and some of their properties are studied. Some properties of the hypergeometric and Bessel matrix functions are obtained.

Canonical State Representations and Hilbert Functions of Multidimensional Systems

A Canonical Matrix Representation of 2-D Linear Discrete Systems

In this paper, a matrix form analoguous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear control systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of the theory of 2-D linear discrete control systems. Necessary a...

Canonical partition functions for parastatistical systems of any order.

A general formula for the canonical partition function for a system obeying any statistics based on the permutation group is derived. The formula expresses the canonical partition function in terms of sums of Schur functions. (1990)] for parasystems of order two is shown to arise as a special case of our general formula. Our results also yield all the relevant information about the structure of...