Matrix Inequalities
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Matrix Inequalities
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Author : Xingzhi Zhan
language : en
Publisher: Springer
Release Date : 2004-10-20
Matrix Inequalities written by Xingzhi Zhan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-20 with Mathematics categories.
The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.
A Survey Of Matrix Theory And Matrix Inequalities
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Author : Marvin Marcus
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
A Survey Of Matrix Theory And Matrix Inequalities written by Marvin Marcus and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.
Matrix Inequalities For Iterative Systems
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Author : Hanjo Taubig
language : en
Publisher: CRC Press
Release Date : 2017-02-03
Matrix Inequalities For Iterative Systems written by Hanjo Taubig and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-03 with Mathematics categories.
The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.
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 Matrix Inequalities
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Author : Mohammad Bagher Ghaemi
language : en
Publisher: Springer Nature
Release Date : 2021-07-11
Advances In Matrix Inequalities written by Mohammad Bagher Ghaemi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-11 with Mathematics categories.
This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.
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.
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.
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 Matrices 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
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Author : Chitra
language : en
Publisher:
Release Date : 2024-01-30
Matrix Inequalities written by Chitra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-30 with Mathematics categories.
In mathematics, inequalities have always being a powerful tool. It remains a major mathematical physics research area beginning with Gauss, Cauchy and oth- ers. Matrix inequalities appears in various fields such as system and control theory [30], optimization [98], mathematical physics [18], statistics [84], economics [95] and engineering disciplines [36]. A wide variety of problems arising in system and con- trol theory can be reduced to a few standard convex or quasi-convex optimization problems involving linear matrix inequalities. Matrix inequalities also play a vital role in quantum statistical inference and quantum information theory (see [17, 78] and references within). As may be deduced from the title, "Matrix Inequalities", various topics such as matrix inequalities of indefinite form, inequalities involving matrix means, Kadison type inequality via matrix means and generalised Furuta's inequality are presented in the thesis.
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.