Matrices

Abstract

Matrix algebra is a branch of mathematics in which numbers are dealt with collectively (as rectangular arrays of numbers called matrices) rather than individually, as in “ordinary” algebra. The term matrix is formally defined in Section 1.1. Section 1.1 also includes an introduction to various basic terminology used in referring to matrices. And some basic matrix operations (scalar multiplication, matrix addition and subtraction, matrix multiplication, and transposition) are defined and their properties discussed in Section 1.2—not all of the properties of the multiplication of ordinary numbers extend to matrix multiplication.

There are many different types of matrices that are sometimes singled out in the literature for special attention. Some of the most basic of these are introduced in Section 1.3. Various other types of matrices are introduced later in the book (as the need arises). In addition, there are many types of matrices that have received considerable attention in the literature but were regarded as too specialized to be considered here.