TY  - BOOK
AU  - Shaked-Monderer,Naomi
AU  - 
AU  - Berman,Abraham
AU  - 
TI  - Copositive and completely positive matrices
SN  - 9789811204340
U1  - 512.943 23
PY  - 2021///
CY  - London
PB  - World Scientific Pub Co Inc
KW  - Matrices
N1  - Revision of: Completely positive matrices / Abraham Berman, Naomi Shaked-Monderer. c2003; Includes bibliographical references and index; Background:
Matrix Theoretic Background
Positive Semidefinite Matrices
Nonnegative Matrices and M-Matrices
Schur Complements
Graphs
Convex Cones
Optimization and the Karush-Kuhn-Tucker Conditions
The PSD Completion Problem
Copositivity:
Definition and Basic Properties
Spectral Properties of Copositive Matrices
Cones of Copositive Matrices
Zeros of Copositive Matrices
M-Irreducibility, Exceptionality and Extremality
Methods for Determining Copositivity
Almost Copositive Matrices
Copositive {0,1,–1}-Matrices and Related Matrices
Small Copositive Matrices
COP₅
Exceptional Extremal Copositive Matrices
The Inverse of a Copositive Matrix
The COP and SPN Completion Problems
SPN Graphs
Complete Positivity:
Definition and Basic Properties
Cones of Completely Positive Matrices
Small Completely Positive Matrices
Complete Positivity and the Comparison Matrix
Completely Positive Graphs
Completely Positive Matrices Whose Graphs are Not Completely Positive
CP₅
Square and Rank-Revealing CP Factorizations
Functions of Completely Positive Matrices
The CP Completion Problem
Rational and Integral completely Positive Matrices
CP-Rank:
Definition and Basic Results
Completely Positive Matrices of a Given Rank
The CP-Ranks and Minimal CP Factorizations in CPₙ
Completely Positive Matrices of a Given Order, with a Given Graph
Bounding Pₙ
When is the CP-Rank Equal to the Rank?
Graphs Attaining minimal CP-Rank
The Number of (Minimal) CP Factorizations
Rational and Integral CP-Rank
The Structure of COP₅ and CP₅:
The Structure of the Copositive Cone
The Structure of CP₅
N2  - "This book is an updated and extended version of Completely Positive Matrices (Abraham Berman and Naomi Shaked-Monderer, World Scientific 2003). It contains new sections on the cone of copositive matrices, which is the dual of the cone of completely positive matrices, and new results on both copositive matrices and completely positive matrices. The book is an up to date comprehensive resource for researchers in Matrix Theory and Optimization. It can also serve as a textbook for an advanced undergraduate or graduate course"--
ER  -