Copositive and completely positive matrices / Naomi Shaked-Monderer, The Max Stern Yezreel Valley College, Israel, Abraham Berman, Technion--Israel Institute of Technology, Israel.

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Contributor(s):

Material type: Text

TextLanguage: English Publication details: London : World Scientific Pub Co Inc, c2021.Edition: Revised editionDescription: pages cmISBN:

9789811204340

Uniform titles:

Completely positive matrices

Subject(s):

DDC classification:

512.943 23 SHA

Contents:

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

Summary: "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"--

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode
Project book	CUTN Central Library	512.943 SHA (Browse shelf(Opens below))	Checked out to Renuka Devi V (20019T)	31/01/2024	48822

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

"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"--

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