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Extreme copositive quadratic forms

Citation

Baumert, Leonard Daniel (1965) Extreme copositive quadratic forms. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-01132003-105545

Abstract

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 [...].

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hall, Marshall
Thesis Committee:
  • Unknown, Unknown
Defense Date:20 October 1964
Record Number:CaltechETD:etd-01132003-105545
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-01132003-105545
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:148
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:13 Jan 2003
Last Modified:26 Dec 2012 02:27

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