Linear Algebra and Matrix Theory

Linear Algebra and Matrix Theory
Author: Robert R. Stoll
Publisher: Courier Corporation
Total Pages: 290
Release: 2012-10-17
Genre: Mathematics
ISBN: 0486623181

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.

Linear Algebra and Matrix Theory

Linear Algebra and Matrix Theory
Author: Jimmie Gilbert
Publisher: Elsevier
Total Pages: 405
Release: 2014-06-28
Genre: Mathematics
ISBN: 0080510256

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.

Linear Algebra and Matrix Analysis for Statistics

Linear Algebra and Matrix Analysis for Statistics
Author: Sudipto Banerjee
Publisher: CRC Press
Total Pages: 586
Release: 2014-06-06
Genre: Mathematics
ISBN: 1420095382

Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.

Linear Algebra: Theory and Applications

Linear Algebra: Theory and Applications
Author: Kenneth Kuttler
Publisher: The Saylor Foundation
Total Pages: 503
Release: 2012-01-29
Genre: Mathematics
ISBN:

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual.

Matrix Analysis and Applied Linear Algebra

Matrix Analysis and Applied Linear Algebra
Author: Carl D. Meyer
Publisher: SIAM
Total Pages: 729
Release: 2000-06-01
Genre: Mathematics
ISBN: 0898714540

This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook.

Finite-Dimensional Vector Spaces

Finite-Dimensional Vector Spaces
Author: Paul R. Halmos
Publisher: Courier Dover Publications
Total Pages: 209
Release: 2017-05-24
Genre: Mathematics
ISBN: 0486822265

Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.

Matrix Theory

Matrix Theory
Author: Fuzhen Zhang
Publisher: Springer Science & Business Media
Total Pages: 290
Release: 2013-03-14
Genre: Mathematics
ISBN: 1475757972

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.

Applied Linear Algebra and Matrix Analysis

Applied Linear Algebra and Matrix Analysis
Author: Thomas S. Shores
Publisher: Springer Science & Business Media
Total Pages: 394
Release: 2007-03-12
Genre: Mathematics
ISBN: 0387489479

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.