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Matrix Theory A Second Course
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Book Synopsis Matrix Theory: A Second Course by : James M. Ortega
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.
Book Synopsis Linear Algebra and Matrices: Topics for a Second Course by : Helene Shapiro
Download or read book Linear Algebra and Matrices: Topics for a Second Course written by Helene Shapiro and published by American Mathematical Soc.. This book was released on 2015-10-08 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.
Book Synopsis A Second Course in Linear Algebra by : Stephan Ramon Garcia
Download or read book A Second Course in Linear Algebra written by Stephan Ramon Garcia and published by Cambridge University Press. This book was released on 2017-05-11 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.
Download or read book Matrix Theory written by James M. Ortega and published by . This book was released on 2014-01-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Matrix Theory written by Robert Piziak and published by CRC Press. This book was released on 2007-02-22 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.
Book Synopsis Linear Algebra and Matrix Theory by : Jimmie Gilbert
Download or read book Linear Algebra and Matrix Theory written by Jimmie Gilbert and published by Elsevier. This book was released on 2014-06-28 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for a serious first course or a second course, this textbook will carry students beyond eigenvalues and eigenvectors to the classification of bilinear forms, to normal matrices, to spectral decompositions, and to the Jordan form. The authors approach their subject in a comprehensive and accessible manner, presenting notation and terminology clearly and concisely, and providing smooth transitions between topics. The examples and exercises are well designed and will aid diligent students in understanding both computational and theoretical aspects. In all, the straightest, smoothest path to the heart of linear algebra. * Special Features: * Provides complete coverage of central material. * Presents clear and direct explanations. * Includes classroom tested material. * Bridges the gap from lower division to upper division work. * Allows instructors alternatives for introductory or second-level courses.
Book Synopsis Introduction to Modern Algebra and Matrix Theory by : O. Schreier
Download or read book Introduction to Modern Algebra and Matrix Theory written by O. Schreier and published by Courier Corporation. This book was released on 2013-05-13 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text provides students with a basic course in both calculus and analytic geometry. It promotes an intuitive approach to calculus and emphasizes algebraic concepts. Minimal prerequisites. Numerous exercises. 1951 edition.
Download or read book Matrix Analysis written by Roger A. Horn and published by Cambridge University Press. This book was released on 1990-02-23 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.
Download or read book Matrix Theory written by Xingzhi Zhan and published by American Mathematical Soc.. This book was released on 2013-06-28 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix theory is a classical topic of algebra that had originated, in its current form, in the middle of the 19th century. It is remarkable that for more than 150 years it continues to be an active area of research full of new discoveries and new applicat
Book Synopsis Linear Algebra and Matrix Theory by : Robert R. Stoll
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.
Book Synopsis The Theory of Matrices by : Peter Lancaster
Download or read book The Theory of Matrices written by Peter Lancaster and published by Academic Press. This book was released on 1985-05-28 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A First Course in Random Matrix Theory by : Marc Potters
Download or read book A First Course in Random Matrix Theory written by Marc Potters and published by Cambridge University Press. This book was released on 2020-12-03 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Book Synopsis Matrix Groups for Undergraduates by : Kristopher Tapp
Download or read book Matrix Groups for Undergraduates written by Kristopher Tapp and published by American Mathematical Soc.. This book was released on 2016-04-07 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots. This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.
Book Synopsis A Survey of Matrix Theory and Matrix Inequalities by : Marvin Marcus
Download or read book A Survey of Matrix Theory and Matrix Inequalities written by Marvin Marcus and published by Courier Corporation. This book was released on 1992-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.
Download or read book Matrix Analysis written by Roger A. Horn and published by Cambridge University Press. This book was released on 2012-10-22 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
Book Synopsis Introduction to Matrix Theory by : Arindama Singh
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.
