MATRICES AND Matrix algebra

A matrix is an m × n array of numbers, typically displayed as

where the entry in row i and column j is denoted as a _ij. Symbolically, we write Av = (a _ij), for i = 1,..., m and j = 1,..., n. A vector is a one-dimensional array, either a row or a column. A column vector is an m × 1 matrix, while a row vector is a 1 × n matrix. For a matrix Av, its ith row vector is usually de-noted by av′_i and its jth column by av_j. Thus an m × n matrix can be decomposed into a set of m row n-vectors or a set of n column m-vectors. Matrices are a natural generalization of single numbers, or scalars. They arise directly or indirectly in most problems in operations research and management science.

BASIC OPERATIONS AND LAWS OF MATRIX ALGEBRA

The language for manipulating matrices is matrix algebra. Matrix algebra is a multivariable extension of single-variable algebra. The basic building block for matrix algebra is the scalar product. The scalar product av · bv of av and bv is a single number (a scalar)...