ABSTRACT
Systems of linear algebraic equations (or simply linear systems) arise in numerous applications; often, these systems appear to have high dimension. This chapter outlines different forms of consistent linear systems and illustrates those with examples, and provides a concise yet rigorous review of the material from linear algebra. It introduces the notion of conditioning of a linear operator (matrix) and that of the corresponding system of linear algebraic equations, and subsequently describes several direct methods for solving linear systems. The chapter discusses what types of numerical algorithms (and why) are better suited for solving particular classes of linear systems. Additionally, it establishes a relation between the systems of linear algebraic equations and the problem of minimization of multi-variable quadratic functions.
