Basic Matrix Theory

Author : Fuzhen Zhang
Publisher : Springer Science & Business Media
ISBN 13 : 1475757972
Total Pages : 290 pages
Book Rating : 4.72/5 ( download)

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Download or read book Matrix Theory written by Fuzhen Zhang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume concisely presents fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The only prerequisites are a decent background in elementary linear algebra and calculus.

Author : Leonard E. Fuller
Publisher : Courier Dover Publications
ISBN 13 : 0486818462
Total Pages : 257 pages
Book Rating : 4.67/5 ( download)

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Download or read book Basic Matrix Theory written by Leonard E. Fuller and published by Courier Dover Publications. This book was released on 2017-09-13 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This guide to using matrices as a mathematical tool offers a model for procedure rather than an exposition of theory. Detailed examples illustrate the focus on computational methods. 1962 edition.

Author : Arindama Singh
Publisher : Springer Nature
ISBN 13 : 303080481X
Total Pages : 199 pages
Book Rating : 4.17/5 ( download)

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Download or read book Introduction to Matrix Theory written by Arindama Singh and published by Springer Nature. This book was released on 2021-08-16 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to serve as a textbook for courses offered to undergraduate and postgraduate students enrolled in Mathematics. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least-squares solutions. The book includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. Most of these problems are theoretical, and they do not fit into the running text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate mathematics courses.

Author : Robert R. Stoll
Publisher : Courier Corporation
ISBN 13 : 0486623181
Total Pages : 290 pages
Book Rating : 4.84/5 ( download)

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Download or read book Linear Algebra and Matrix Theory written by Robert R. Stoll and published by Courier Corporation. This book was released on 2012-10-17 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.

Author : Joel N. Franklin
Publisher : Courier Corporation
ISBN 13 : 0486136388
Total Pages : 319 pages
Book Rating : 4.87/5 ( download)

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Download or read book Matrix Theory written by Joel N. Franklin and published by Courier Corporation. This book was released on 2012-07-31 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.

Author : James M. Ortega
Publisher : Springer Science & Business Media
ISBN 13 : 9780306424335
Total Pages : 278 pages
Book Rating : 4.39/5 ( download)

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Download or read book Matrix Theory: A Second Course written by James M. Ortega and published by Springer Science & Business Media. This book was released on 1987-02-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.

Author : Feliks Ruvimovich Gantmakher
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.55/5 ( download)

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Download or read book The Theory of Matrices written by Feliks Ruvimovich Gantmakher and published by . This book was released on 1964 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : James E. Gentle
Publisher : Springer Science & Business Media
ISBN 13 : 0387708723
Total Pages : 536 pages
Book Rating : 4.20/5 ( download)

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Download or read book Matrix Algebra written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2007-07-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Rajendra Bhatia
Publisher : Springer Science & Business Media
ISBN 13 : 1461206537
Total Pages : 360 pages
Book Rating : 4.38/5 ( download)

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Download or read book Matrix Analysis written by Rajendra Bhatia and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.

Author : Howard Eves
Publisher : Courier Corporation
ISBN 13 : 0486150275
Total Pages : 356 pages
Book Rating : 4.77/5 ( download)

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Download or read book Elementary Matrix Theory written by Howard Eves and published by Courier Corporation. This book was released on 2012-04-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The usefulness of matrix theory as a tool in disciplines ranging from quantum mechanics to psychometrics is widely recognized, and courses in matrix theory are increasingly a standard part of the undergraduate curriculum. This outstanding text offers an unusual introduction to matrix theory at the undergraduate level. Unlike most texts dealing with the topic, which tend to remain on an abstract level, Dr. Eves' book employs a concrete elementary approach, avoiding abstraction until the final chapter. This practical method renders the text especially accessible to students of physics, engineering, business and the social sciences, as well as math majors. Although the treatment is fundamental — no previous courses in abstract algebra are required — it is also flexible: each chapter includes special material for advanced students interested in deeper study or application of the theory. The book begins with preliminary remarks that set the stage for the author's concrete approach to matrix theory and the consideration of matrices as hypercomplex numbers. Dr. Eves then goes on to cover fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, similarity and congruence. A final optional chapter considers matrix theory from a generalized or abstract viewpoint, extending it to arbitrary number rings and fields, vector spaces and linear transformations of vector spaces. The author's concluding remarks direct the interested student to possible avenues of further study in matrix theory, while an extensive bibliography rounds out the book. Students of matrix theory will especially appreciate the many excellent problems (solutions not provided) included in each chapter, which are not just routine calculation exercises, but involve proof and extension of the concepts and material of the text. Scientists, engineers, economists and others whose work involves this important area of mathematics, will welcome the variety of special types of matrices and determinants discussed, which make the book not only a comprehensive introduction to the field, but a valuable resource and reference work.