Baumert, Leonard Daniel (1965) Extreme copositive quadratic forms. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-01132003-105545
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|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||20 October 1964|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||13 Jan 2003|
|Last Modified:||26 Dec 2012 02:27|
- Final Version
See Usage Policy.
Repository Staff Only: item control page