Copositive And Completely Positive Matrices
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Copositive And Completely Positive Matrices
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Author : Naomi Shaked-monderer
language : en
Publisher: World Scientific
Release Date : 2021-02-09
Copositive And Completely Positive Matrices written by Naomi Shaked-monderer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-09 with Mathematics categories.
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.
Completely Positive Matrices
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Author : Abraham Berman
language : en
Publisher: World Scientific
Release Date : 2003
Completely Positive Matrices written by Abraham Berman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A = BBOC is known as the cp- rank of A . This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp- rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined. Contents: Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M -Matrices; Schur Complements; Graphs; Convex Cones; The PSD Completion Problem; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Matrices; 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 CP Completion Problem; 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?. Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory."
Matrix Positivity
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Author : Charles R. Johnson
language : en
Publisher: Cambridge University Press
Release Date : 2020-10
Matrix Positivity written by Charles R. Johnson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10 with Mathematics categories.
This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.
Tensor Analysis
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Author : Liqun Qi
language : en
Publisher: SIAM
Release Date : 2017-04-19
Tensor Analysis written by Liqun Qi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-19 with Mathematics categories.
Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors.
Positive Linear Maps Of Operator Algebras
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Author : Erling Størmer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-13
Positive Linear Maps Of Operator Algebras written by Erling Størmer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-13 with Mathematics categories.
This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.
Completely Positive Matrices
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Author : Abraham Berman
language : en
Publisher: World Scientific
Release Date : 2003-04-11
Completely Positive Matrices written by Abraham Berman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-11 with Mathematics categories.
A real matrix is positive semidefinite if it can be decomposed as A=BB′. In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BB′ is known as the cp-rank of A.This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp-rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined.
Semidefinite Optimization And Convex Algebraic Geometry
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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21
Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
An Introduction To Semi Tensor Product Of Matrices And Its Applications
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Author : Dai-Zhan Cheng
language : en
Publisher: World Scientific
Release Date : 2012
An Introduction To Semi Tensor Product Of Matrices And Its Applications written by Dai-Zhan Cheng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
A generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations.This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.
Matrix Methods
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Author : Vadim Olshevsky
language : en
Publisher: World Scientific
Release Date : 2010
Matrix Methods written by Vadim Olshevsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume. --
Matrix Partial Orders Shorted Operators And Applications
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Author : Sujit Kumar Mitra
language : en
Publisher: World Scientific
Release Date : 2010
Matrix Partial Orders Shorted Operators And Applications written by Sujit Kumar Mitra and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
1. Introduction. 1.1. Matrix orders. 1.2. Parallel sum and shorted operator. 1.3. A tour through the rest of the monograph -- 2. Matrix decompositions and generalized inverses. 2.1. Introduction. 2.2. Matrix decompositions. 2.3. Generalized inverse of a matrix. 2.4. The group inverse. 2.5. Moore-Penrose inverse. 2.6. Generalized inverses of modified matrices. 2.7. Simultaneous diagonalization. 2.8. Exercises -- 3. The minus order. 3.1. Introduction. 3.2. Space pre-order. 3.3. Minus order - some characterizations. 3.4. Matrices above/below a given matrix under the minus order. 3.5. Subclass of g-inverses A[symbol] of A such that [symbol]A = A[symbol]B and AA[symbol]=BA[symbol] when A