Date of Award


Document Type


Degree Name

Master of Science

Degree Discipline



The theory of matrices occupies a strategic position both in pure and in applied mathematics. They are used in applications in physics, economics, engineering, and others. In pure mathematics, matrices also play a great role.

This paper concerns itself with the bilinear and quadratic forms, Quadratic forms occur not only in the study of conic sections and quadric surfaces in Analytic Geometry but also in problems of maxima and minima, dynamics, and statistics, as well as throughout higher mathematics.

In this paper, we shall show that any quadratic form may be written as the sum of squares, Given any quadratic form (1) it can be written in matrix notation such that the coefficient matrix will be symmetric and (2) the eigenmumbers are real and (3) if the eigennumbers are distinct, there exist a matrix P, such that P AP-1 = D where D is the diagonal matrix or (4) there exist a symmetric matrix B of rank r, there exist a P such that PBP- 1 = D. Therefore we claim that the quadratic form will have the form.

Committee Chair/Advisor

A. D. Stewart


Prairie View Agricultural and Mechanical College


© 2021 Prairie View A & M University

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Date of Digitization


Contributing Institution

John B Coleman Library

City of Publication

Prairie View




To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.