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From Dimension Free Matrix Theory To Cross Dimensional Dynamic Systems

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From Dimension Free Matrix Theory To Cross Dimensional Dynamic Systems

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Author : Daizhan Cheng
language : en
Publisher: Academic Press
Release Date : 2019-05-18

From Dimension Free Matrix Theory To Cross Dimensional Dynamic Systems written by Daizhan Cheng and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-18 with Mathematics categories.

From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems feature prominently across many disciplines, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and biosystems, deep learning, IT, and information-based engineering applications. - Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems. - Offers potential applications to the analysis and control of new dimension-varying systems. - Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.

Matrix And Operator Equations And Applications

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Author : Mohammad Sal Moslehian
language : en
Publisher: Springer Nature
Release Date : 2023-07-29

Matrix And Operator Equations And Applications written by Mohammad Sal Moslehian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-29 with Mathematics categories.

This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades. The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations. In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed. In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed. The chapters give a comprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

A Dynamical Approach To Random Matrix Theory

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Author : László Erdős
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-30

A Dynamical Approach To Random Matrix Theory written by László Erdős 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 2017-08-30 with Mathematics categories.

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Scientific And Technical Aerospace Reports

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Author :
language : en
Publisher:
Release Date : 1991

Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Aeronautics categories.

Large Space Structures Systems In The Space Station Era

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Author :
language : en
Publisher:
Release Date : 1993

Large Space Structures Systems In The Space Station Era written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Large space structures (Astronautics) categories.

Echinoderms Munchen

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Author : Thomas Heinzeller
language : en
Publisher: CRC Press
Release Date : 2005-12-08

Echinoderms Munchen written by Thomas Heinzeller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-08 with Science categories.

Since 1972, scientists from all over the world working on fundamental questions of echinoderm biology and palaeontology have conferred every three years to exchange current views and results. The 11th International Echinoderm Conference held at the University of Munich, Germany, from 6-10 October 2003,continued this tradition. This volume comprises 95 submitted papers and 96 abstracts covering a wide spectrum from innovative student contributions to the lessons learnt from experienced specialists. The content of the contributions ranges from original research results to the latest synopses concerning a variety of topics, including visual sensing, larval cloning, mutable collagenous tissues, sea urchin aqua-culture, deuterostome phylogeny, palaeobiology and taphonomy.