Author: Fuzhen Zhang
Publisher: Springer Science & Business Media
ISBN: 1475757972
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
Book Description
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: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486623181
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
Book Description
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: 0486136388
Category : Mathematics
Languages : en
Pages : 319
Get Book Here
Book Description
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: Marvin Marcus
Publisher: Courier Corporation
ISBN: 9780486671024
Category : Mathematics
Languages : en
Pages : 212
Get Book Here
Book Description
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.
Author: David Lewis
Publisher: World Scientific Publishing Company
ISBN: 9813103477
Category : Mathematics
Languages : en
Pages : 310
Get Book Here
Book Description
This book provides an introduction to matrix theory and aims to provide a clear and concise exposition of the basic ideas, results and techniques in the subject. Complete proofs are given, and no knowledge beyond high school mathematics is necessary. The book includes many examples, applications and exercises for the reader, so that it can used both by students interested in theory and those who are mainly interested in learning the techniques.
Author: Roger A. Horn
Publisher: Cambridge University Press
ISBN: 9780521386326
Category : Mathematics
Languages : en
Pages : 580
Get Book Here
Book Description
Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.
Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 0821874306
Category : Mathematics
Languages : en
Pages : 298
Get Book Here
Book Description
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
Author: Marc Potters
Publisher: Cambridge University Press
ISBN: 1108488080
Category : Computers
Languages : en
Pages : 371
Get Book Here
Book Description
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Author: Robert Piziak
Publisher: CRC Press
ISBN: 1584886250
Category : Mathematics
Languages : en
Pages : 570
Get Book Here
Book Description
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: Jinho Baik
Publisher: American Mathematical Soc.
ISBN: 0821848410
Category : Mathematics
Languages : en
Pages : 478
Get Book Here
Book Description
Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.
