Completely positive matrices / Abraham Berman, Naomi Shaked-Monderer.

Format:

Book

Author/Creator:

Berman, Abraham.

Contributor:

Shaked-Monderer, Naomi.

J. Fithian Tatem Memorial Fund.

Language:

English

Subjects (All):

Matrices.

Physical Description:

ix, 206 pages : illustrations ; 24 cm

Place of Publication:

[River Edge] New Jersey : World Scienfic, [2003]

Summary:

Completely positive matrices (not to be confused with the completely positive maps in operator theory) arise from the related concept of completely positive quadratic forms in the theory of block designs. In this graduate or advanced undergraduate text, Berman (Israel Institute of Technology) and Shaked-Monderer (Emek Yezteel College) describe the conditions necessary and sufficient for complete positivity and the bounds for the cp-rank. They present the material in modules within three chapters, with topics ranging from preliminary studies on theory, complex positivity and analysis of the cp-rank. They include exercise and a list of notations. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Contents:

1.1 Matrix theoretic background 1

1.2 Positive semidefinite matrices 9

1.3 Nonnegative matrices and M-matrices 18

1.4 Schur complements 24

1.5 Graphs 30

1.6 Convex cones 41

1.7 The PSD completion problem 56

Chapter 2 Complete positivity 61

2.2 Cones of completely positive matrices 71

2.3 Small matrices 73

2.4 Complete positivity and the comparison matrix 78

2.5 Completely positive graphs 83

2.6 Completely positive matrices whose graphs are not completely positive 97

2.7 Square factorizations 122

2.8 Functions of completely positive matrices 129

2.9 The CP completion problem 133

Chapter 3 CP rank 139

3.2 Completely positive matrices of a given rank 146

3.3 Completely positive matrices of a given order 156

3.4 When is the cp-rank equal to the rank? 177.

Notes:

Includes bibliographical references (pages 193-197) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the J. Fithian Tatem Memorial Fund.

ISBN:

9812383689

OCLC:

52718561