Null Structure and Interpolation Problems for Matrix Polynomials

Abstract

In this chapter we consider matrix polynomials, i.e. matrix functions L(z) of the form $L(z) = \sum\nolimits_{i = 0}^e {{A_i}{z^i},}$ where A ₀ A _l,..., A _ℓ are n × n matrices. We will assume throughout also that L(z) is regular, i.e. det L(z) does not vanish identically. One of our aims is to specify for matrix polynomials in a detailed way the theory developed in the first chapter for analytic matrix functions. We also solve here the first interpolation problem in this book, namely, how to construct a matrix polynomial with given null structure. Explicit formulas for the solution are obtained.