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Selected methods of matrix inversion
Couger, Patricia A.
Couger, Patricia A.
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1956-05
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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.
Table of Contents
Introduction -- Matrix operations and definitions -- Cayley-Hamilton method of matrix inversion -- Modified Gauss-Doolittle method of matrix inversion -- Choolesy's scheme for matrix inversitn -- Summary -- Bibliography
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Thesis (M.A.)-- University of Wichita, College of Liberal Arts and Sciences, Dept. of Mathematics
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Wichita State University
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Wichita State University