Details

Extreme copositive quadratic forms

by Baumert, Leonard Daniel

Abstract (Summary)
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. A real quadratic form [...] is called copositive if [...] whenever [...]. If we associate each quadratic form [...] with a point [...] of Euclidean [...] space, then the copositive forms constitute a closed convex cone in this space. We are concerned with the extreme points of this cone. That is, with those copositive quadratic forms Q for which [...] implies [...]. We show that (1) If [...] is an extreme copositive quadratic form then for any index pair [...] has a zero [...] with [...]. (2) If [...] is an extreme copositive quadratic form in [...] variables [...] then replacing [...] in [...] yields a new copositive form [...] which is also extreme. (3) If [...] is an extreme copositive quadratic form then either (i) Q is positive semi-definite, or (ii) Q is related to an extreme form discovered by A. Horn, or (iii) Q possesses exactly five zeros having non-negative components. In this later case the zeros can be assumed to be [...] and [...] where [...].
Bibliographical Information:

Advisor:Marshall Hall

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis

Keywords:mathematics

ISBN:

Date of Publication:10/20/1964

© 2009 OpenThesis.org. All Rights Reserved.