Geometry Of Linear Matrix Inequalities

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Geometry Of Linear Matrix Inequalities

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Author : Tim Netzer
language : en
Publisher: Springer Nature
Release Date : 2023-06-07

Geometry Of Linear Matrix Inequalities written by Tim Netzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-07 with Mathematics categories.

This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can be represented and approximated as spectrahedra and their shadows (projections). Several general results obtained in the last 15 years by a variety of different methods are presented in the book, along with the necessary background from algebra and geometry.

Linear Matrix Inequalities In System And Control Theory

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Author : Stephen Boyd
language : en
Publisher: SIAM
Release Date : 1994-01-01

Linear Matrix Inequalities In System And Control Theory written by Stephen Boyd and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.

In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.

Advances In Linear Matrix Inequality Methods In Control

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Author : Laurent El Ghaoui
language : en
Publisher: SIAM
Release Date : 2000-01-01

Advances In Linear Matrix Inequality Methods In Control written by Laurent El Ghaoui and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.

Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control.

Dilations Linear Matrix Inequalities The Matrix Cube Problem And Beta Distributions

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Author : J. William Helton
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-02-21

Dilations Linear Matrix Inequalities The Matrix Cube Problem And Beta Distributions written by J. William Helton and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Mathematics categories.

An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V:H→K such that C=V∗TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor ϑ(d), expressed as a ratio of Γ functions for d even, of all d×d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space.

Matrix Inequalities And Their Extensions To Lie Groups

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Author : Tin-Yau Tam
language : en
Publisher: CRC Press
Release Date : 2018-03-14

Matrix Inequalities And Their Extensions To Lie Groups written by Tin-Yau Tam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-14 with Mathematics categories.

Matrix Inequalities and Their Extensions to Lie Groups gives a systematic and updated account of recent important extensions of classical matrix results, especially matrix inequalities, in the context of Lie groups. It is the first systematic work in the area and will appeal to linear algebraists and Lie group researchers.

A Course In Convexity

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Author : Alexander Barvinok
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-11-19

A Course In Convexity written by Alexander Barvinok and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-19 with Mathematics categories.

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.

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 Matrix Concentration Inequalities

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Author : Joel Tropp
language : en
Publisher:
Release Date : 2015-05-27

An Introduction To Matrix Concentration Inequalities written by Joel Tropp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-27 with Computers categories.

Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.

Matrix Information Geometry

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Author : Frank Nielsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-07

Matrix Information Geometry written by Frank Nielsen 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 2012-08-07 with Technology & Engineering categories.

This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems engineering. The topics and application include Information Geometry, Differential Geometry of structured Matrix, Positive Definite Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and Applications in Cognitive systems, in particular Data Mining.

Linear Algebra And Geometry

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Author : Igor R. Shafarevich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-23

Linear Algebra And Geometry written by Igor R. Shafarevich 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 2012-08-23 with Mathematics categories.

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.