Index Matrices: Towards an Augmented Matrix Calculus, Krassimir T. Atanassov

Автор: Bhatia Rajendra
Название: Positive Definite Matrices
ISBN: 0691168253 ISBN-13(EAN): 9780691168258
Издательство: Wiley
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Описание: This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical enginee

Автор: Friedland Shmuel
Название: Matrices: Algebra, Analysis and Applications
ISBN: 981466796X ISBN-13(EAN): 9789814667968
Издательство: World Scientific Publishing
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Цена: 30096.00 р.
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Описание: This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics.

Автор: Duff I. S
Название: Direct Methods for Sparse Matrices
ISBN: 0198508387 ISBN-13(EAN): 9780198508380
Издательство: Oxford Academ
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Описание: The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This book provides both insight and answers for those attempting to solve these problems.

Автор: Su Zhonggen
Название: Random Matrices And Random Partitions: Normal Convergence
ISBN: 9814612227 ISBN-13(EAN): 9789814612227
Издательство: World Scientific Publishing
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Описание: This Book Is Aimed At Graduate Students And Researchers Who Are Interested In The Probability Limit Theory Of Random Matrices And Random Partitions. It Mainly Consists Of Three Parts. Part I Is A Brief Review Of Classical Central Limit Theorems For Sums Of Independent Random Variables, Martingale Sequences And Markov Chains, Etc. These Classical Theorems Are Frequently Used In The Study Of Random Matrices And Random Partitions Where Random Matrices Are Well-Studied In Probability Theory. Part Ii Concentrates On The Asymptotic Distribution Theory Of Circular Unitary Ensemble And Gaussian Unitary Ensemble, Which Are Prototypes Of Random Matrix Theory. It Turns Out That The Classical Central Limit Theorems And Methods Are Applicable In Describing Asymptotic Distributions Of Eigenvalue Statistics Like Linear Functionals Of Eigenvalues. This Is Attributed To The Nice Algebraic Structures Of Models. This Part Also Studies The Circular β Ensembles And Gaussian β Ensembles, Which May Be Viewed As Extensions Of The Circular Unitary Ensemble And Gaussian Unitary Ensemble. Part Iii Is Devoted To The Study Of Random Uniform And Plancherel Partitions. As Is Known, There Is A Surprising Similarity Between Random Matrices And Random Integer Partitions From The Viewpoint Of Asymptotic Distribution Theory, Though It Is Difficult To Find Any Direct Link Between The Two Finite Models.This Book Treats Only Second-Order Fluctuations For Primary Random Variables From Two Classes Of Special Random Models. It Is Written In A Clear, Concise And Pedagogical Way. It May Be Read As An Introductory Text To Further Study Probability Theory Of General Random Matrices, Random Partitions And Even Random Point Processes. This Book Is Aimed At Graduate Students And Researchers Who Are Interested In Probability Limit Theory Of Random Matrices And Random Integer Partitions.