Introduction To Matrix Theory

Author : Arindama Singh
Publisher : Springer Nature
Page : 199 pages
File Size : 52,7 Mb
Release : 2021-08-16
Category : Mathematics
ISBN : 9783030804817

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Introduction to Matrix Theory by Arindama Singh Pdf

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 : Fumio Hiai,Dénes Petz
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 47,9 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.

Author : Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
Publisher : Springer
Page : 124 pages
File Size : 43,6 Mb
Release : 2018-01-16
Category : Science
ISBN : 9783319708850

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Introduction to Random Matrices by Giacomo Livan,Marcel Novaes,Pierpaolo Vivo Pdf

Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.

Author : O. Schreier,E. Sperner
Publisher : Courier Corporation
Page : 402 pages
File Size : 40,8 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486278650

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Introduction to Modern Algebra and Matrix Theory by O. Schreier,E. Sperner Pdf

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.

Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 482 pages
File Size : 42,5 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9783030528119

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Introduction to Linear and Matrix Algebra by Nathaniel Johnston Pdf

This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 290 pages
File Size : 49,8 Mb
Release : 2012-10-17
Category : Mathematics
ISBN : 9780486623184

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Linear Algebra and Matrix Theory by Robert R. Stoll Pdf

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 : Ferenc Szidarovszky,S ndor Moln r
Publisher : World Scientific
Page : 516 pages
File Size : 43,6 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.

Author : Fuzhen Zhang
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 49,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475757972

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Matrix Theory by Fuzhen Zhang Pdf

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 : Peter M. Higgins
Publisher : Oxford University Press, USA
Page : 161 pages
File Size : 46,8 Mb
Release : 2015
Category : Algebra
ISBN : 9780198732822

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Algebra by Peter M. Higgins Pdf

This introduction invites readers to revisit algebra and appreciate the elegance and power of equations and inequalities. Offering a clear explanation of algebra through theory and example, Higgins shows how equations lead to complex numbers, matrices, groups, rings, and fields.--

Author : Richard Bellman
Publisher : SIAM
Page : 424 pages
File Size : 54,6 Mb
Release : 1997-12-01
Category : Mathematics
ISBN : 9780898713992

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Introduction to Matrix Analysis by Richard Bellman Pdf

Lucid and concise, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods.

Author : Robert Piziak,P.L. Odell
Publisher : CRC Press
Page : 570 pages
File Size : 51,8 Mb
Release : 2007-02-22
Category : Mathematics
ISBN : 9781584886259

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Matrix Theory by Robert Piziak,P.L. Odell Pdf

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.

Author : Leonard E. Fuller
Publisher : Courier Dover Publications
Page : 256 pages
File Size : 48,9 Mb
Release : 2017-05-25
Category : Mathematics
ISBN : 9780486822624

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Basic Matrix Theory by Leonard E. Fuller Pdf

Written as a guide to using matrices as a mathematical tool, this text is geared toward physical and social scientists, engineers, economists, and others who require a model for procedure rather than an exposition of theory. Knowledge of elementary algebra is the only mathematical prerequisite. Detailed numerical examples illustrate the treatment's focus on computational methods. The first four chapters outline the basic concepts of matrix theory. Topics include the development of the concept of elementary operations and a systematic procedure for simplifying matrices as well as a method for evaluating the determinant of a given square matrix. Subsequent chapters explore important numerical procedures, including the process for approximating characteristic roots and vectors plus direct and iterative methods for inverting matrices and solving systems of equations. Solutions to the problems are included.

Author : Jacob T. Schwartz
Publisher : Courier Corporation
Page : 198 pages
File Size : 46,5 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486143705

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Introduction to Matrices and Vectors by Jacob T. Schwartz Pdf

Realizing that matrices can be a confusing topic for the beginner, the author of this undergraduate text has made things as clear as possible by focusing on problem solving, rather than elaborate proofs. He begins with the basics, offering students a solid foundation for the later chapters on using special matrices to solve problems.The first three chapters present the basics of matrices, including addition, multiplication, and division, and give solid practice in the areas of matrix manipulation where the laws of algebra do not apply. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. He also covers special matrices — including complex numbers, quaternion matrices, and matrices with complex entries — and transpose matrices; the trace of a matrix; the cross product of matrices; eigenvalues and eigenvectors; and infinite series of matrices. Exercises at the end of each section give students further practice in problem solving. Prerequisites include a background in algebra, and in the later chapters, a knowledge of solid geometry. The book was designed as an introductory text for college freshmen and sophomores, but selected chapters can also be used to supplement advanced high school classes. Professionals who need a better understanding or review of the subject will also benefit from this concise guide.

Author : 王正盛
Publisher : Unknown
Page : 148 pages
File Size : 40,7 Mb
Release : 2015
Category : Mathematical analysis
ISBN : 7030453948

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Introduction to Matrix Theory by 王正盛 Pdf

Author : Greg W. Anderson,Alice Guionnet,Ofer Zeitouni
Publisher : Cambridge University Press
Page : 507 pages
File Size : 46,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780521194525

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An Introduction to Random Matrices by Greg W. Anderson,Alice Guionnet,Ofer Zeitouni Pdf

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.