Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis

Strong Linearizations of Rational Matrices

This paper defines for the first time strong linearizations of arbitrary rational matrices, studies in depth properties and different characterizations of such linear matrix pencils, and develops infinitely many examples of strong linearizations that can be explicitly and easily constructed from a minimal state-space realization of the strictly proper part of the considered rational matrix and ...

On the characterization and parametrization of strong linearizations of polynomial matrices

Rational and Polynomial Matrices

where λ = s or λ = z for a continuousor discrete-time realization, respectively. It is widely accepted that most numerical operations on rational or polynomial matrices are best done by manipulating the matrices of the corresponding descriptor system representations. Many operations on standard matrices (such as finding the rank, determinant, inverse or generalized inverses, nullspace) or the s...

Orthogonal Rational Functions and Structured Matrices

The space of all proper rational functions with prescribed poles is considered. Given a set of points zi in the complex plane and the weights wi, we define the discrete inner product

A Basis-Kernel Representation of Orthogonal Matrices

In this paper we introduce a new representation of orthogonal matrices. We show that any orthogonal matrix can be represented in the form Q = I ? Y SY T , which we call the basis-kernel representation of Q. We show that the kernel S can be chosen to be triangular and show how the familiar representation of an orthogonal matrix as a product of Householder matrices can be directly derived from a ...