Application Of Matrices To The Reduction Of Bilinear And Quadratic Forms To Sums Of Squares (Canonical Form)

Author

Frank A. Kincade, Prairie View Agricultural and Mechanical College

Date of Award

8-1962

Document Type

Thesis

Degree Name

Master of Science

Degree Discipline

Mathematics

Abstract

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

Publisher

Prairie View Agricultural and Mechanical College

Rights

Date of Digitization

11/19/2021

Contributing Institution

John B Coleman Library

City of Publication

Prairie View

MIME Type

Application/PDF

Recommended Citation

Kincade, F. A. (1962). Application Of Matrices To The Reduction Of Bilinear And Quadratic Forms To Sums Of Squares (Canonical Form). Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/744