TABLE OF CONTENTS In this section, some results from matrix algebra that are useful in our development in this book are summarized. Most of the matrix properties presented in this section are elementary and can be found in standard texts on matrix algebra. Therefore, most of the properties presented below are quoted without proof.
An m n matrix A is an ordered rectangular array that has m n elements. This array is written as
The element a ij lies in the ith row and jth column of the matrix A. Therefore, the index i, which takes the values 1, 2, ..., m, denotes the row number, while the index j, which takes the values 1, 2, ..., n, denotes the column number. A matrix is said to be a square matrix if m = n. The transpose of the matrix A, denoted by A T, is the matrix given by
Thus A T is an n m matrix.
The sum of two matrices A and B, denoted by A + B, is given by
where b ij are the elements of B. To add two matrices A and B, it is necessary that A and B have the same number of rows and columns. It is clear that matrix addition is...
