2 - Elementary Matrix Methods

Abstract

An array of numbers or functions ordered according to m-rows and n-columns is known as a matrix of order m×n and is denoted by “A.” The matrix containing only one row or one column is said to be a vector, a row vector, or a column vector respectively. The matrices present a useful compact algorithm that can be implemented on the electronic calculators. Matrices are important for solving systems of linear algebraic equations and for dealing a compact notation with linear transformations from one set of variables to another set. Their algebra is linear and simple. Matrices in quantum mechanics represent the linear Hermitian operators that describe the quantities that can be observed by experiments. Some properties of the determinants are: if all the elements of a row or column are zero, or if two rows or two columns are identical, the determinant vanishes. This chapter reviews various types of special matrices such as: the null matrix, the diagonal matrix, the scalar matrix, and the identity matrix.