Handbook of Linear Algebra, 2nd Edition

Chapter 19

Matrix Equations

Beatrice Meini

Università di Pisa

Matrix equations are equations involving matrices, both in the unknown and in the formal expression of the equation. They appear in various guises: linear and polynomial matrix equations, in the form of matrix power series, of rational functions, and more. The interest is both in the theoretical properties and in the numerical solution, since many matrix equations arise in the modeling of real world problems. In this chapter, after giving an introduction with several examples, we analyze linear matrix equations, polynomial matrix equations, and algebraic Riccati equations.

Unless differently specified, all the matrices in this chapter are complex.

19.1 Introduction

Definitions:

In ...