On The Roots Of Matrices

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Matrices And Their Roots: A Textbook Of Matrix Algebra

Author : A R G Heesterman
Publisher : World Scientific Publishing Company
ISBN 13 : 9813103639
Total Pages : 476 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Matrices And Their Roots: A Textbook Of Matrix Algebra by : A R G Heesterman

Download or read book Matrices And Their Roots: A Textbook Of Matrix Algebra written by A R G Heesterman and published by World Scientific Publishing Company. This book was released on 1990-12-31 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook addresses itself to two groups of students who need mathematics in an applied context: undergraduates starting at the beginning, and postgraduates who need reference-material, but who, not being mathematics specialists, nevertheless are not best served by an ordinary mathematics textbook, which will generally be at a higher level of abstraction. It gives full proofs throughout, and is illustrated with a large number of numerical examples, reinforcing the student's grasp of the topics covered by exercises and corresponding answersheets, and by the corresponding tutorial program ILLUSTRATE. The program ‘Illustrate’ will run on any IBM compatible micro-computer. The relevant areas of application are economics, econometrics, mathematical programming and engineering.

Functions of Matrices

Author : Nicholas J. Higham
Publisher : SIAM
ISBN 13 : 0898717779
Total Pages : 445 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Functions of Matrices by : Nicholas J. Higham

Download or read book Functions of Matrices written by Nicholas J. Higham and published by SIAM. This book was released on 2008-01-01 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.

Matrices and Their Roots

Author : A. R. G. Heesterman
Publisher : World Scientific
ISBN 13 : 9789810203962
Total Pages : 472 pages
Book Rating : 4.2/5 (39 download)

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Book Synopsis Matrices and Their Roots by : A. R. G. Heesterman

Download or read book Matrices and Their Roots written by A. R. G. Heesterman and published by World Scientific. This book was released on 1990 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook addresses itself to two groups of students who need mathematics in an applied context: undergraduates starting at the beginning, and postgraduates who need reference-material, but who, not being mathematics specialists, nevertheless are not best served by an ordinary mathematics textbook, which will generally be at a higher level of abstraction. It gives full proofs throughout, and is illustrated with a large number of numerical examples, reinforcing the student's grasp of the topics covered by exercises and corresponding answersheets, and by the corresponding tutorial program ILLUSTRATE. The program ?Illustrate? will run on any IBM compatible micro-computer. The relevant areas of application are economics, econometrics, mathematical programming and engineering.

Lambda-matrices and Vibrating Systems

Author : Peter Lancaster
Publisher : Courier Corporation
ISBN 13 : 9780486425467
Total Pages : 226 pages
Book Rating : 4.4/5 (254 download)

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Book Synopsis Lambda-matrices and Vibrating Systems by : Peter Lancaster

Download or read book Lambda-matrices and Vibrating Systems written by Peter Lancaster and published by Courier Corporation. This book was released on 2002-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers several aspects and solutions of the problems of linear vibrating systems with a finite number of degrees of freedom. It offers a detailed account of the part of the theory of matrices necessary for efficient problem-solving, beginning with a focus on developing the necessary tools in matrix theory in the first four chapters. The following chapters present numerical procedures for the relevant matrix formulations and the relevant theory of differential equations. Directed toward a wide audience of applied mathematicians, scientists, and engineers, this book has much to offer all those interested in problem-solving from both practical and theoretical points of view. The mathematically sound treatment involves readers in a minimum of mathematical abstraction; it assumes a familiarity and facility with matrix theory, along with a knowledge of elementary calculus (including the rudiments of the theory of functions of a complex variable). Those already engaged in the practical analysis of vibrating systems have the option of proceeding directly to the more applications-oriented material, starting with Chapter 7; however, this comprehensive treatment offers ample background in the early chapters for less experienced readers. New Preface to the Dover Edition. Errata List. Preface. Bibliographical Notes. References. Index.

KWIC Index for Numerical Algebra

Author : Alston Scott Householder
Publisher :
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis KWIC Index for Numerical Algebra by : Alston Scott Householder

Download or read book KWIC Index for Numerical Algebra written by Alston Scott Householder and published by . This book was released on 1972 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applications of the Theory of Matrices

Author : F. R. Gantmacher
Publisher : Courier Corporation
ISBN 13 : 0486445542
Total Pages : 336 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Applications of the Theory of Matrices by : F. R. Gantmacher

Download or read book Applications of the Theory of Matrices written by F. R. Gantmacher and published by Courier Corporation. This book was released on 2005-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Around the Unit Circle

Author : James McKee
Publisher : Springer Nature
ISBN 13 : 3030800318
Total Pages : 444 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Around the Unit Circle by : James McKee

Download or read book Around the Unit Circle written by James McKee and published by Springer Nature. This book was released on 2021-12-08 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.

A First Course in Linear Algebra

Author : Kenneth Kuttler
Publisher :
ISBN 13 :
Total Pages : 586 pages
Book Rating : 4.:/5 (125 download)

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Book Synopsis A First Course in Linear Algebra by : Kenneth Kuttler

Download or read book A First Course in Linear Algebra written by Kenneth Kuttler and published by . This book was released on 2020 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook."--BCcampus website.

Intermediate Algebra 2e

Author : Lynn Marecek
Publisher :
ISBN 13 : 9781951693848
Total Pages : pages
Book Rating : 4.6/5 (938 download)

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Book Synopsis Intermediate Algebra 2e by : Lynn Marecek

Download or read book Intermediate Algebra 2e written by Lynn Marecek and published by . This book was released on 2020-05-06 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Applied Linear Algebra

Author : Stephen Boyd
Publisher : Cambridge University Press
ISBN 13 : 1316518965
Total Pages : 477 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

American Journal of Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis American Journal of Mathematics by :

Download or read book American Journal of Mathematics written by and published by . This book was released on 1919 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.

Nonnegative Matrices in the Mathematical Sciences

Author : Abraham Berman
Publisher : Academic Press
ISBN 13 : 1483260860
Total Pages : 337 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Nonnegative Matrices in the Mathematical Sciences by : Abraham Berman

Download or read book Nonnegative Matrices in the Mathematical Sciences written by Abraham Berman and published by Academic Press. This book was released on 2014-05-10 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.

An Introduction to Random Matrices

Author : Greg W. Anderson
Publisher : Cambridge University Press
ISBN 13 : 0521194520
Total Pages : 507 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis An Introduction to Random Matrices by : Greg W. Anderson

Download or read book An Introduction to Random Matrices written by Greg W. Anderson and published by Cambridge University Press. This book was released on 2010 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

Matrix Operations for Engineers and Scientists

Author : Alan Jeffrey
Publisher : Springer Science & Business Media
ISBN 13 : 9048192749
Total Pages : 323 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Matrix Operations for Engineers and Scientists by : Alan Jeffrey

Download or read book Matrix Operations for Engineers and Scientists written by Alan Jeffrey and published by Springer Science & Business Media. This book was released on 2010-09-05 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of their properties a simple matter, and in practical applications such software is often essential. However, using this tool when learning about matrices, without first gaining a proper understanding of the underlying theory, limits the ability to use matrices and to apply them to new problems. This book explains matrices in the detail required by engineering or science students, and it discusses linear systems of ordinary differential equations. These students require a straightforward introduction to linear algebra illustrated by applications to which they can relate. It caters of the needs of undergraduate engineers in all disciplines, and provides considerable detail where it is likely to be helpful. According to the author the best way to understand the theory of matrices is by working simple exercises designed to emphasize the theory, that at the same time avoid distractions caused by unnecessary numerical calculations. Hence, examples and exercises in this book have been constructed in such a way that wherever calculations are necessary they are straightforward. For example, when a characteristic equation occurs, its roots (the eigenvalues of a matrix) can be found by inspection. The author of this book is Alan Jeffrey, Emeritus Professor of mathematics at the University of Newcastle upon Tyne. He has given courses on engineering mathematics at UK and US Universities.

Graphs and Matrices

Author : Ravindra B. Bapat
Publisher : Springer
ISBN 13 : 1447165691
Total Pages : 197 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Graphs and Matrices by : Ravindra B. Bapat

Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.

Toeplitz and Circulant Matrices

Author : Robert M. Gray
Publisher : Now Publishers Inc
ISBN 13 : 1933019239
Total Pages : 105 pages
Book Rating : 4.9/5 (33 download)

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Book Synopsis Toeplitz and Circulant Matrices by : Robert M. Gray

Download or read book Toeplitz and Circulant Matrices written by Robert M. Gray and published by Now Publishers Inc. This book was released on 2006 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.

The Theory of Matrices in Numerical Analysis

Author : Alston S. Householder
Publisher : Courier Corporation
ISBN 13 : 0486145638
Total Pages : 274 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Theory of Matrices in Numerical Analysis by : Alston S. Householder

Download or read book The Theory of Matrices in Numerical Analysis written by Alston S. Householder and published by Courier Corporation. This book was released on 2013-06-18 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents selected aspects of matrix theory that are most useful in developing computational methods for solving linear equations and finding characteristic roots. Topics include norms, bounds and convergence; localization theorems; more. 1964 edition.