Introduction

As we said in the preface, linear algebra is everywhere in numerical simulations, often well hidden for the average user, but always crucial in terms of performance and efficiency. Almost all numerical computations in physics, mechanics, chemistry, engineering, economics, finance, etc., involve numerical linear algebra, i.e., computations involving matrices. The purpose of this introduction is to give a few examples of applications of the two main types of matrix computations: solving linear systems of equations on the one hand, and computing eigenvalues and eigenvectors on the other hand. The following examples serve as a motivation for the main notions, methods, and algorithms discussed in this book.