Selected methods of matrix inversion

Abstract

Matrix theory is concerned with the study of rectangular arrays of elements called matrices . In this paper, except for one example, no attempt will be made to describe how these arrays are obtained originally nor to discuss what the numbers might represent . From the outset, an array of numbers will be given, and it will be desired to determine another array which is called the inverse of the given array. In the second chapter a formal definition of a matrix will be given, and special types of matrices will be defined . The basic operations of addition and multiplication of matrices will be defined . Finally, the definition of an inverse will be presented along with one method for computing the 'inverse. In the third, fourth, and fifth chapters, there will be presented three other methods which can be used to determine the inverse of a matrix. As an example these methods are illustrated for a square matrix having six rows and six columns . A summary of these methods and a discussion of certain other available methods will follow in the sixth chapter.