Generalized Inverses of Polynomial Matrices

Abstract

A polynomial matrix is a matrix whose entries are polynomials. Equivalently, a polynomial matrix can be expressed as a polynomial with matrix coefficients. Formally speaking, in the univariable case, $(\mathbb {R}[x])^{m \times n}$ and $(\mathbb {R}^{m \times n}) [x]$ are isomorphic. In other words, extending the entries of matrices to polynomials is the same as extending the coefficients of polynomials to matrices.