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Author : Stephan Ramon Garcia,Roger A. Horn
Publisher : Cambridge University Press
Page : 447 pages
File Size : 46,8 Mb
Release : 2017-05-11
Category : Mathematics
ISBN : 9781107103818
A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.
Author : Helene Shapiro
Publisher : American Mathematical Soc.
Page : 317 pages
File Size : 49,9 Mb
Release : 2015-10-08
Category : Mathematics
ISBN : 9781470418526
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.
Author : William Clough Brown
Publisher : Wiley-Interscience
Page : 298 pages
File Size : 42,6 Mb
Release : 1988
Category : Mathematics
ISBN : UVA:X001401506
This textbook for senior undergraduate and first year graduate-level courses in linear algebra and analysis, covers linear algebra, multilinear algebra, canonical forms of matrices, normal linear vector spaces and inner product spaces. These topics provide all of the prerequisites for graduate students in mathematics to prepare for advanced-level work in such areas as algebra, analysis, topology and applied mathematics.
Author : Irving Kaplansky
Publisher : Courier Corporation
Page : 182 pages
File Size : 46,8 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0486432335
The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition.
Author : Kenneth Kuttler,Ilijas Farah
Publisher : Unknown
Page : 586 pages
File Size : 40,7 Mb
Release : 2020
Category : Algebras, Linear
ISBN : OCLC:1252786692
"A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook."--BCcampus website.
Author : Sheldon Axler
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 41,6 Mb
Release : 1997-07-18
Category : Mathematics
ISBN : 0387982590
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Author : James M. Ortega
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 53,7 Mb
Release : 1987-02-28
Category : Mathematics
ISBN : 0306424339
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 : David B. Damiano,John B. Little
Publisher : Courier Corporation
Page : 466 pages
File Size : 41,7 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780486469089
"Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter contains an introduction, definitions, and propositions, in addition to multiple examples, lemmas, theorems, corollaries, andproofs. Each chapter features numerous supplemental exercises, and solutions to selected problems appear at the end. 1988 edition"--
Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 482 pages
File Size : 41,8 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9783030528119
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 : Serge Lang
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210702
This is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, while others are conceptual.
Author : Kuldeep Singh
Publisher : Oxford University Press
Page : 617 pages
File Size : 43,5 Mb
Release : 2013-10
Category : Mathematics
ISBN : 9780199654444
"This book is intended for first- and second-year undergraduates arriving with average mathematics grades ... The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to all of the set problems freely available online http://www.oup.co.uk/companion/singh" -- From preface.
Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 48,8 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author : Steven Roman
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 54,9 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780387274744
Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra
Author : T.S. Blyth,E.F. Robertson
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 46,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781447106814
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers: this will take the form of a tutorial on the use of the "LinearAlgebra" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.
Author : Mohammed K A Kaabar
Publisher : CreateSpace Independent Publishing Platform
Page : 130 pages
File Size : 42,9 Mb
Release : 2014-10-20
Category : Mathematics
ISBN : 9781502901811
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It is also included exercises at the end of each chapter above to let students practice additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at “Answers to Odd-Numbered Exercises” section at the end of this book. This book is very useful for college students who studied Calculus I, and other students who want to review some linear algebra concepts before studying a second course in linear algebra.
