Title: The Real Positive Definite Completion Problem: Cycle Completability (Memoirs of the American Mathematical Society)
Publisher: Amer Mathematical Society
Publication Date: 1996
Language: English
ISBN 10: 0821804731
ISBN 13: 9780821804735
Binding: Paperback
Condition: Good
Dust Jacket Condition: No Jacket
Weight: 0.35 pounds

About this title

Synopsis

Given a partial symmetric matrix, the positive definite completion problem asks if the unspecified entries in the matrix can be chosen so as to make the resulting matrix positive definite. Applications include probability and statistics, image enhancement, systems engineering, geophysics, and mathematical programming. The positive definite completion problem can also be viewed as a mechanism for addressing a fundamental problem in Euclidean geometry: which potential geometric configurations of vectors (i.e., configurations with angles between some vectors specified) are realizable in a Euclidean space. The positions of the specified entries in a partial matrix are naturally described by a graph. The question of existence of a positive definite completion was previously solved completely for the restrictive class of chordal graphs and this work solves the problem for the class of cycle completable graphs, a significant generalization of chordal graphs. These are the graphs for which knowledge of completability for induced cycles (and cliques) implies completability of partial symmetric matrices with the given graph.

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