Baumert, Leonard Daniel (1965) Extreme copositive quadratic forms. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd01132003105545
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 semidefinite, or (ii) Q is related to an extreme form discovered by A. Horn, or (iii) Q possesses exactly five zeros having nonnegative 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 
Major Option:  Mathematics 
Thesis Committee: 

Defense Date:  20 October 1964 
Record Number:  etd01132003105545 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd01132003105545 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  148 
Collection:  CaltechTHESES 
Deposited By:  Imported from ETDdb 
Deposited On:  13 Jan 2003 
Last Modified:  25 Dec 2012 14:57 
Thesis Files

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