TABLE OF CONTENTS This appendix summarizes the definitions, operations, and properties of matrices that are used in the book. More detailed treatments of matrices, along with proofs for the properties stated in this appendix, can be found in [1; 2; 3; 4].
An N M matrix A is a rectangular array of values with N rows and M columns, written as
The (ij)th element (or entry) of A (i.e., the element in the ith row and jth column) is written as A ij . In (C.1) we have A ij = a ij . The matrix elements are also called scalars to indicate that they are single numbers. An N M matrix is called a square matrix if N = M, a skinny matrix if N > M, and a fat matrix if N < M.
The diagonal elements of a matrix are the elements along the diagonal line starting from the top left of the matrix (i.e., the elements A ij with i = j). The trace of a square N N matrix is the sum of its diagonal elements: 
. A square matrix is called a diagonal matrix if all elements that are not diagonal elements, referred to as the off-diagonal elements, are zero: A ij = 0, j ? i. We...
