Linear Algebra And Matrix Theory

Author : Jimmie Gilbert,Linda Gilbert
Publisher : Elsevier
Page : 394 pages
File Size : 46,9 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080510255

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Linear Algebra and Matrix Theory by Jimmie Gilbert,Linda Gilbert Pdf

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.

Author : I. N. Herstein,David J. Winter
Publisher : MacMillan Publishing Company
Page : 536 pages
File Size : 54,9 Mb
Release : 1988
Category : Mathematics
ISBN : UOM:39015053340132

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Matrix Theory and Linear Algebra by I. N. Herstein,David J. Winter Pdf

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 290 pages
File Size : 53,7 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 : Carl D. Meyer
Publisher : SIAM
Page : 729 pages
File Size : 42,8 Mb
Release : 2000-06-01
Category : Mathematics
ISBN : 9780898714548

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Matrix Analysis and Applied Linear Algebra by Carl D. Meyer Pdf

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.

Author : Sudipto Banerjee,Anindya Roy
Publisher : CRC Press
Page : 586 pages
File Size : 47,7 Mb
Release : 2014-06-06
Category : Mathematics
ISBN : 9781420095388

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Linear Algebra and Matrix Analysis for Statistics by Sudipto Banerjee,Anindya Roy Pdf

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.

Author : Kenneth Kuttler
Publisher : The Saylor Foundation
Page : 503 pages
File Size : 48,7 Mb
Release : 2012-01-29
Category : Mathematics
ISBN : 8210379456XXX

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Linear Algebra: Theory and Applications by Kenneth Kuttler Pdf

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.

Author : Evar D. Nering
Publisher : Unknown
Page : 352 pages
File Size : 49,8 Mb
Release : 1970
Category : Algebras, Linear
ISBN : LCCN:07691646

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Linear Algebra and Matrix Theory by Evar D. Nering Pdf

Author : James M. Ortega
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 45,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489904713

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Matrix Theory: A Second Course by James M. Ortega Pdf

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 : Paul R. Halmos
Publisher : Princeton University Press
Page : 196 pages
File Size : 44,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882236

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Finite Dimensional Vector Spaces. (AM-7), Volume 7 by Paul R. Halmos Pdf

As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."

Author : Fuzhen Zhang
Publisher : World Scientific
Page : 477 pages
File Size : 48,7 Mb
Release : 2021-10-25
Category : Mathematics
ISBN : 9789811239106

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Problems In Linear Algebra And Matrix Theory by Fuzhen Zhang Pdf

This is the revised and expanded edition of the problem book Linear Algebra: Challenging Problems for Students, now entitled Problems in Linear Algebra and Matrix Theory. This new edition contains about fifty-five examples and many new problems, based on the author's lecture notes of Advanced Linear Algebra classes at Nova Southeastern University (NSU-Florida) and short lectures Matrix Gems at Shanghai University and Beijing Normal University.The book is intended for upper division undergraduate and beginning graduate students, and it can be used as text or supplement for a second course in linear algebra. Each chapter starts with Definitions, Facts, and Examples, followed by problems. Hints and solutions to all problems are also provided.

Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 482 pages
File Size : 53,9 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 : Fuzhen Zhang
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 55,6 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 : O. Schreier,E. Sperner
Publisher : Courier Corporation
Page : 402 pages
File Size : 51,9 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 : Hans Schneider,George Phillip Barker
Publisher : Courier Corporation
Page : 432 pages
File Size : 48,6 Mb
Release : 2012-06-08
Category : Mathematics
ISBN : 9780486139302

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Matrices and Linear Algebra by Hans Schneider,George Phillip Barker Pdf

Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues, and differential equations. Includes numerous exercises.

Author : Israel N. Herstein,David J. Winter
Publisher : Unknown
Page : 508 pages
File Size : 46,7 Mb
Release : 1989
Category : Algebras, Linear
ISBN : 0029461545

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Matrix Theory and Linear Algebra by Israel N. Herstein,David J. Winter Pdf