1. Background in Matrix Theory and Linear Algebra
Yousef El-Mabruk Saad · Society for Industrial and Applied Mathematics eBooks · 2011
This chapter reviews basic matrix theory and introduces some of the elementary notation used throughout the book. Matrices are objects that represent linear mappings between vector spaces. The notions that will be predominantly used in this book are very intimately related to these linear mappings and it is possible to discuss eigenvalues of linear operators without ever mentioning their matrix representations. However, to the numerical analyst, or the engineer, any theory that would be developed in this manner would be insufficient in that it will not be of much help in developing or understanding computational algorithms. The abstraction of linear mappings on vector spaces does however provide very concise definitions and some important theorems.