Copositive And Completely Positive Matrices

by Naomi Shaked-monderer, Abraham Berman

Overview

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.

Product Details

ISBN-13:	9789811204340
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	03/19/2021
Pages:	564
Product dimensions:	6.00(w) x 9.00(h) x 1.25(d)

Table of Contents

Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M-Matrices; Schur Complement ; Graphs; Convex Cones; The PSD Completion Problem; Copositivity: Definition and Basic Properties; Spectral Properties of Copositive Matrices; The Copositive Cone; Zeros of Copositive Matrices; Copositivity Characterization; Almost Copositive Matrices; Copositive {0,1,-1}-Matrices; Small Copositive Matrices; COP5; The Inverse of a Copositive Matrix; The Geometry of the Copositive Cone; The COP and SPN Completion Problems; SPN Graphs; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Completely Positive Matrices; Completely Positive Matrices of Order 5; Complete Positivity and the Comparison Matrix; Completely Positive Graphs; Completely Positive Matrices Whose Graphs are Not Completely Positive; Square Factorizations; Functions of Completely Positive Matrices; The Geometry of the Completely Positive Cone; The CP and DNN Completion Problems; The CP-Rank: Definition and Basic Results; Completely Positive Matrices of a Given Rank; Completely Positive Matrices of a Given Order; When is the CP-Rank Equal to the Rank?; C(O)P Optimization?