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Type of Document	Dissertation
Author	Baumert, Leonard Daniel
URN	etd-01132003-105545
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-01132003-105545
Title	Extreme copositive quadratic forms
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Marshall Hall Committee Chair
Keywords	None
Date of Defense	1964-10-20
Availability	unrestricted
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 [...].
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    Baumert_ld_1965.pdf 2.24 Mb 00:10:23 00:05:20 00:04:40 00:02:20 00:00:11