Chapter I - MATRICES

Abstract

This chapter describes matrices. A matrix is a rectangular array of elements arranged in horizontal rows and vertical columns. If the matrix has as many rows (p) as columns (n), p = n, then it is called a square matrix. The elements of a matrix need not be numbers; they can be, and quite often arise physically as, functions, operators, or matrices themselves. A matrix is an entity unto itself; it is not a number. The simplest relationship between two matrices is equality. Intuitively one feels that two matrices should be equal if their corresponding elements are equal. This is the case providing the matrices are of the same order. Two matrices are not multiplied together element-wise. It is not always possible to multiply the matrices of the same order, while it is possible to multiply certain matrices of different orders. The chapter reviews as to which matrices can be multiplied together and how this operation is to be performed.