Applications Of The Theory Of Matrices

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Applications of the Theory of Matrices

F. R. Gantmacher,J.L. Brenner
Applications of the Theory of Matrices Book PDF

Author : F. R. Gantmacher,J.L. Brenner
Publisher : Courier Corporation
Page : 336 pages
File Size : 42,8 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 9780486445540

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Applications of the Theory of Matrices by F. R. Gantmacher,J.L. Brenner Pdf

The breadth of matrix theory's applications is reflected by this volume, which features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Starting with a survey of complex symmetric, antisymmetric, and orthogonal matrices, the text advances to explorations of singular bundles of matrices and matrices with nonnegative elements. Applied mathematicians will take particular note of the full and readable chapter on applications of matrix theory to the study of systems of linear differential equations, and the text concludes with an exposition on the Routh-Hurwitz problem plus several helpful appendixes. 1959 edition.

The Theory of Matrices

Peter Lancaster,Miron Tismenetsky
The Theory of Matrices Book PDF

Author : Peter Lancaster,Miron Tismenetsky
Publisher : Academic Press
Page : 590 pages
File Size : 45,6 Mb
Release : 1985-05-28
Category : Computers
ISBN : 0124355609

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The Theory of Matrices by Peter Lancaster,Miron Tismenetsky Pdf

Matrix algebra; Determinants, inverse matrices, and rank; Linear, euclidean, and unitary spaces; Linear transformations and matrices; Linear transformations in unitary spaces and simple matrices; The jordan canonical form: a geometric approach; Matrix polynomials and normal forms; The variational method; Functions of matrices; Norms and bounds for eigenvalues; Perturbation theory; Linear matrices equations and generalized inverses; Stability problems; Matrix polynomials; Nonnegative matrices.

Matrices

Denis Serre
Matrices Book PDF

Author : Denis Serre
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 55,6 Mb
Release : 2010-10-26
Category : Mathematics
ISBN : 1441976833

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Matrices by Denis Serre Pdf

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.

The Theory of Matrices

Peter Lancaster,Miron Tismenetsky
The Theory of Matrices Book PDF

Author : Peter Lancaster,Miron Tismenetsky
Publisher : Elsevier
Page : 570 pages
File Size : 53,8 Mb
Release : 1985-05-24
Category : Mathematics
ISBN : 9780080519081

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The Theory of Matrices by Peter Lancaster,Miron Tismenetsky Pdf

In this book the authors try to bridge the gap between the treatments of matrix theory and linear algebra. It is aimed at graduate and advanced undergraduate students seeking a foundation in mathematics, computer science, or engineering. It will also be useful as a reference book for those working on matrices and linear algebra for use in their scientific work.

Matrix Theory and Applications

Charles R. Johnson
Matrix Theory and Applications Book PDF

Author : Charles R. Johnson
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 43,7 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821801543

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Matrix Theory and Applications by Charles R. Johnson Pdf

This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.

Matrix Algebra

James E. Gentle
Matrix Algebra Book PDF

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 54,7 Mb
Release : 2007-07-27
Category : Computers
ISBN : 9780387708720

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Matrix Algebra by James E. Gentle Pdf

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Matrix Theory with Applications

Jack Leonard Goldberg
Matrix Theory with Applications Book PDF

Author : Jack Leonard Goldberg
Publisher : McGraw-Hill Companies
Page : 552 pages
File Size : 49,8 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015047513323

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Matrix Theory with Applications by Jack Leonard Goldberg Pdf

This course, generally called Linear Algebra, is usually taught in mathematics departments as a service course for engineers. While there is no real prerequisite other than algebra, students will need a calculus of differential equations background to appreciate this course.

Introduction to Matrix Analysis and Applications

Fumio Hiai,Dénes Petz
Introduction to Matrix Analysis and Applications Book PDF

Author : Fumio Hiai,Dénes Petz
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 54,7 Mb
Release : 2014-02-06
Category : Mathematics
ISBN : 9783319041506

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Introduction to Matrix Analysis and Applications by Fumio Hiai,Dénes Petz Pdf

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.

Introduction to Matrix Theory

Ferenc Szidarovszky,S ndor Moln r
Introduction to Matrix Theory Book PDF

Author : Ferenc Szidarovszky,S ndor Moln r
Publisher : World Scientific
Page : 516 pages
File Size : 44,7 Mb
Release : 2002
Category : Business & Economics
ISBN : 9810245130

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Introduction to Matrix Theory by Ferenc Szidarovszky,S ndor Moln r Pdf

In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields.

Applications of Matrix Theory

M. J. C. Gover,S. Barnett,Stephen Barnett
Applications of Matrix Theory Book PDF

Author : M. J. C. Gover,S. Barnett,Stephen Barnett
Publisher : Unknown
Page : 352 pages
File Size : 40,8 Mb
Release : 1989
Category : Algebras, Linear
ISBN : UCAL:B5008691

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Applications of Matrix Theory by M. J. C. Gover,S. Barnett,Stephen Barnett Pdf

This unique volume surveys the current state of research in matrix theory and applied linear algebra. It provides information on matrix approximation and factorization, matrices in optimization theory, the theory of sparse matrices, and matrix theory in statistics, with careful attention to numerical computation and the impact of parallelism of matrix computations. This comprehensive work is an invaluable reference for researchers in all areas of applied mathematics.

Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

Jason J. Molitierno
Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs Book PDF

Author : Jason J. Molitierno
Publisher : CRC Press
Page : 425 pages
File Size : 40,6 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781439863398

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Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs by Jason J. Molitierno Pdf

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

Matrices

Denis Serre
Matrices Book PDF

Author : Denis Serre
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 55,6 Mb
Release : 2007-12-18
Category : Mathematics
ISBN : 9780387227580

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Matrices by Denis Serre Pdf

Clear and concise introduction to matrices with elegant proofs; Of interest to scientists from many disciplines; Gives many interesting applications to different parts of mathematics, such as algebra, analysis and complexity theory; Contains 160 exercises, half of them on advanced material; Includes at least one advanced result per chapter

Density Matrix Theory and Applications

Karl Blum
Density Matrix Theory and Applications Book PDF

Author : Karl Blum
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 46,9 Mb
Release : 2013-06-29
Category : Science
ISBN : 9781461568087

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Density Matrix Theory and Applications by Karl Blum Pdf

Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary vari ables. The use of density matrix methods also has the advantage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incom~'\etely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.

Nonnegative Matrices and Applications

R. B. Bapat,T. E. S. Raghavan
Nonnegative Matrices and Applications Book PDF

Author : R. B. Bapat,T. E. S. Raghavan
Publisher : Cambridge University Press
Page : 351 pages
File Size : 40,9 Mb
Release : 1997-03-28
Category : Mathematics
ISBN : 9780521571678

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Nonnegative Matrices and Applications by R. B. Bapat,T. E. S. Raghavan Pdf

This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

Euclidean Distance Matrices and Their Applications in Rigidity Theory

Abdo Y. Alfakih
Euclidean Distance Matrices and Their Applications in Rigidity Theory Book PDF

Author : Abdo Y. Alfakih
Publisher : Springer
Page : 251 pages
File Size : 42,6 Mb
Release : 2018-10-13
Category : Mathematics
ISBN : 9783319978468

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Euclidean Distance Matrices and Their Applications in Rigidity Theory by Abdo Y. Alfakih Pdf

This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration. Euclidean Distance Matrices and Their Applications in Rigidity Theory begins by establishing the necessary background needed for the rest of the book. The focus of Chapter 1 is on pertinent results from matrix theory, graph theory and convexity theory, while Chapter 2 is devoted to positive semidefinite (PSD) matrices due to the key role these matrices play in our approach. Chapters 3 to 7 provide detailed studies of EDMs, and in particular their various characterizations, classes, eigenvalues and geometry. Chapter 8 serves as a transitional chapter between EDMs and rigidity theory. Chapters 9 and 10 cover local and universal rigidities of bar-and-joint frameworks. This book is self-contained and should be accessible to a wide audience including students and researchers in statistics, operations research, computational biochemistry, engineering, computer science and mathematics.