What Are Matrices

Abstract

In real life, a matrix is a rectangular array with prescribed numbers n of rows and m of columns (n×m matrix). To make this array as clear as possible, one encloses it between delimiters; we choose parentheses in this book. The position at the intersection of the ith row and jth column is labeled by the pair (i, j). If the name of the matrix is M (respectively, A, X, etc.), the entry at the (i, j)th position is usually denoted m _{i j} (respectively, a _{i j} , x _{i j} ). An entry can be anything provided it gives the reader information. Here is a the real-life example.