Matrix Analysis And Applications
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Matrix Analysis And Applications
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Author : Xian-Da Zhang
language : en
Publisher: Cambridge University Press
Release Date : 2017-10-05
Matrix Analysis And Applications written by Xian-Da Zhang 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 2017-10-05 with Computers categories.
The theory, methods and applications of matrix analysis are presented here in a novel theoretical framework.
Introduction To Matrix Analysis And Applications
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Author : Fumio Hiai
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-06
Introduction To Matrix Analysis And Applications written by Fumio Hiai 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 2014-02-06 with Mathematics categories.
Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Fundamentals Of Matrix Analysis With Applications
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Author : Edward Barry Saff
language : en
Publisher: John Wiley & Sons
Release Date : 2015-10-12
Fundamentals Of Matrix Analysis With Applications written by Edward Barry Saff and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-12 with Mathematics categories.
An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.
Matrix Analysis Of Structural Dynamics
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Author : Franklin Y. Cheng
language : en
Publisher: CRC Press
Release Date : 2017-09-06
Matrix Analysis Of Structural Dynamics written by Franklin Y. Cheng and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Technology & Engineering categories.
Uses state-of-the-art computer technology to formulate displacement method with matrix algebra. Facilitates analysis of structural dynamics and applications to earthquake engineering and UBC and IBC seismic building codes.
Matrices
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Author : Denis Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-26
Matrices written by Denis Serre 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 2010-10-26 with Mathematics categories.
In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.
Matrix Algebra
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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-06
Matrix Algebra written by James E. Gentle 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 2007-08-06 with Mathematics categories.
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
Applications Of Combinatorial Matrix Theory To Laplacian Matrices Of Graphs
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Author : Jason J. Molitierno
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Applications Of Combinatorial Matrix Theory To Laplacian Matrices Of Graphs written by Jason J. Molitierno and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Computers categories.
On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o
Applied And Computational Matrix Analysis
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Author : Natália Bebiano
language : en
Publisher: Springer
Release Date : 2017-03-01
Applied And Computational Matrix Analysis written by Natália Bebiano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-01 with Mathematics categories.
This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.
Matrices
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Author : Denis Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Matrices written by Denis Serre 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 2002 with Mathematics categories.
Matrices summarizes much of the basics of matrix theory and then goes on to give many interesting applications of matrices to different parts of mathematics, such as algebra, analysis, complexity theory and the theory of computation. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. It will also provide scientists and mathematicians with a useful and reliable reference.
Hadamard Matrix Analysis And Synthesis
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Author : Rao K. Yarlagadda
language : en
Publisher: Springer
Release Date : 2012-10-10
Hadamard Matrix Analysis And Synthesis written by Rao K. Yarlagadda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-10 with Technology & Engineering categories.
Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal/Image Processing presents the basic concepts of Sylvester's construction of Hadamard matrices, the eigenvalue-eigenvector decompositions, along with its relationship to Fourier transforms. Relevant computational structures are included for those interested in implementing the Hadamard transform. The 2-dimensional Hadamard transform is discussed in terms of a 1- dimensional transform. The applications presented touch on statistics, error correction coding theory, communications signaling, Boolean function analysis and synthesis, image processing, sequence theory (maximal length binary sequences, composite sequences, and Thue-Morse sequences) and signal representation. An interesting application of the Hadamard transform to images is the Naturalness Preserving Transform (NPT), which is presented. The NPT provides a way to encode an image that can be reconstructed when it is transmitted through a noisy or an unfriendly channel. The potential applications of the Hadamard transform are wide and the book samples many of the important concepts among a vast field of applications of the transform. Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal/Image Processing serves as an excellent reference source and may be used as a text for advanced courses on the topic.