Featured Resources
Linear Algebra and its Applications by
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible. Students conceptual understanding is reinforced through True/False questions, practice problems, and the use of technology. David Lay changed the study of linear algebra with the execution of this philosophy, and continues his quest to improve the way linear algebra is taught with the new Updated Second Edition. With this update he takes the instruction of linear algebra to a new level through inc
Call Number: QA184 .L397 2000ISBN: 0201347741Publication Date: 1999-08-11
Linear Algebra by
Praise for the Third Edition "This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications." - Electric Review A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fourth Edition also features: Two new and independent sections on the rapidly developing subject of wavelets A thoroughly updated section on electrical circuit theory Illuminating applications of linear algebra with self-study questions for additional study End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® code Linear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester courses for students majoring in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.
Call Number: E-BOOKISBN: 9781118909584Publication Date: 2015-11-23
Linear Algebra with Applications by
Designed for an introductory course in linear algebra, this text combines theory, computational techniques, and applications. Topics covered include Gauss-Jordan elimination, matrix operations, vectors, dot product, linear transformation, matrix transformations, vector spaces, linear independence, b
Call Number: QA184 .W53 2000ISBN: 0763714518Publication Date: 2000-07-21
Linear Algebra Books & E-Books
Ordinary Differential Equations and Linear Algebra by
Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system. Ordinary Differential Equations and Linear Algebra: Systematically develops the linear algebra needed to solve systems of ODEs. Includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). Emphasizes mathematical modeling. Contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.
Call Number: QA372 .K2155 2015ISBN: 9781611974089Publication Date: 2016-02-25
Matrix Methods by
Matrix Methods: Applied Linear Algebra, Third Edition, as a textbook, provides a unique and comprehensive balance between the theory and computation of matrices. The application of matrices is not just for mathematicians. The use by other disciplines has grown dramatically over the years in response to the rapid changes in technology. Matrix methods is the essence of linear algebra and is what is used to help physical scientists; chemists, physicists, engineers, statisticians, and economists solve real world problems.
Call Number: QA188 .B758 2009ISBN: 9780123744272Publication Date: 2008-12-05
Matrix Theory by
The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields. Major changes in this revised and expanded second edition: -Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms -A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices -A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms.
Call Number: QA188 .Z47 2011ISBN: 9781461410980Publication Date: 2011-08-31
Advanced Topics in Linear Algebra by
The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra.Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin O'Meara, John Clark, and Charles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr formand the Jordan form. Developing an understanding of both forms will allow students and researchers to exploit the mathematical capabilities of each in varying situations.Weaving together ideas and applications from various mathematical disciplines, Advanced Topics in Linear Algebra is much more than a derivation of the Weyr form. It presents novel applications of linear algebra, such as matrix commutativity problems, approximate simultaneous diagonalization, andalgebraic geometry, with the latter two having topical connections to phylogenetic invariants in biomathematics and multivariate interpolation. Among the related mathematical disciplines from which the book draws ideas are commutative and noncommutative ring theory, module theory, field theory,topology, and algebraic geometry. Numerous examples and current open problems are included, increasing the book's utility as a graduate text or as a reference for mathematicians and researchers in linear algebra.
Call Number: E-BOOKISBN: 9780199793730Publication Date: 2011-09-16
Elementary Linear Algebra by
This book ELEMENTARY LINEAR ALGEBRA is a well-organized, lucidly written text introducing the reader to system of equations, vector spaces, linear transformations, eigen values and eigen vectors. In addition, the book presents the subject in a simple manner for easy understanding. A large number of illustrated examples are covered to clarify the theoretical concepts with many unsolved problems for practice to enhance the presentation of the material. The book is suitable for undergraduate students of science and engineering.
Call Number: E-BOOKISBN: 9781842654002Publication Date: 2012-01-01
A Guide to Advanced Linear Algebra by
Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives. Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups. The book treats vector spaces in full generality, though it concentrates on the finite dimensional case. Also, it treats vector spaces over arbitrary fields, specializing to algebraically closed fields or to the fields of real and complex numbers as necessary.
Call Number: E-BOOKISBN: 9780883853511Publication Date: 2011-12-31
Matrix Algebra for Linear Models by
A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra's application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.
Call Number: E-BOOKISBN: 9781118592557Publication Date: 2013-12-31
Linear Algebra by
Linear algebra is a prerequisite for students majoring in mathematics and is required of many undergraduate and first-year graduate students in statistics, engineering, and related areas. This fully updated and revised text defines the discipline's main terms, explains its key theorems, and provides over 425 example problems ranging from the elementary to some that may baffle even the most seasoned mathematicians. Vital concepts are highlighted at the beginning of each chapter and a final section contains hints for solving the problems as well as solutions to each example.Based on Fuzhen Zhang's experience teaching and researching algebra over the past two decades, Linear Algebra is the perfect examination study tool. Students in beginning and seminar-type advanced linear algebra classes and those seeking to brush up on the topic will find Zhang's plain discussions of the subject's theories refreshing and the problems diverse, interesting, and challenging.
Call Number: E-BOOKISBN: 9780801891250Publication Date: 2009-04-07
A (Terse) Introduction to Linear Algebra by
Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications. A (Terse) Introduction to Linear Algebra is a concise presentation of the core material of the subject--those elements of linear algebra that every mathematician, and everyone who uses mathematics, should know. It goes from the notion of a finite-dimensional vector space to the canonical forms of linear operators and their matrices, and covers along the way such key topics as: systems of linear equations, linear operators and matrices, determinants, duality, and the spectral theory of operators on inner-product spaces. The last chapter offers a selection of additional topics indicating directions in which the core material can be applied. The Appendix provides all the relevant background material. Written for students with some mathematical maturity and an interest in abstraction and formal reasoning, the book is self-contained and is appropriate for an advanced undergraduate course in linear algebra.
Call Number: QA184.2 .K38 2008ISBN: 9780821844199Publication Date: 2007-12-19
Applied Linear Algebra by
A useful reference, this book could easily be subtitled: All the Linear Algebra I Learned from Doing Physics that I Wished Somebody had Taught Me First . Built upon the principles of diagonalization and superposition, it contains many important physical applications-such as population growth, normal modes of oscillations, waves, Markov chains, stability analysis, signal processing, and electrostatics-in order to demonstrate the incredible power of linear algebra in the world. The underlying ideas of breaking a vector into modes, and of decoupling a complicated system by suitable choice of linear coordinates, are emphasized throughout the book. Chapter topics most useful to professional engineers and physicists include-but are not limited to-the wave equation, continuos spectra, fourier transforms, and Green's function. For electrical engineers, physicists, and mechanical engineers.
Call Number: QA184 .S23 2001ISBN: 0130856452Publication Date: 2000-08-09
Applied Numerical Linear Algebra by
Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely-used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommendations of which algorithms to use in a variety of practical situations. This is the book for you if you are looking for a textbook that: Teaches state-of-the-art techniques for solving linear algebra problems. Covers the most important methods for dense and sparse problems. Presents both the mathematical background and good software techniques. Is self-contained, assuming only a good undergraduate background in linear algebra. Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in Matlab and are freely available on the Web. Material either not available elsewhere, or presented quite differently in other textbooks, includes: A discussion of the impact of modern cache-based computer memories on algorithm design. Frequent recommendations and pointers in the text to the best software currently available, including a detailed performance comparison of state-of-the-art software for eigenvalue and least squares problems, and a description of sparse direct solvers for serial and parallel machines. A discussion of iterative methods ranging from Jacobi's method to multigrid and domain decomposition, with performance comparisons on a model problem. A great deal of Matlab-based software, available on the Web, which either implements algorithms presented in the book, produces the figures in the book, or is used in homework problems. Numerical examples drawn from fields ranging from mechanical vibrations to computational geometry. High-accuracy algorithms for solving linear systems and eigenvalue problems, along with tighter ""relative"" error bounds. Dynamical systems interpretations of some eigenvalue algorithms. Demmel discusses several current research topics, making students aware of both the lively research taking place and connections to other parts of numerical analysis, mathematics, and computer science. Some of this material is developed in questions at the end of each chapter, which are marked Easy, Medium, or Hard according to their difficulty. Some questions are straightforward, supplying proofs of lemmas used in the text. Others are more difficult theoretical or computing problems. Questions involving significant amounts of programming are marked Programming. The computing questions mainly involve Matlab programming, and others involve retrieving, using, and perhaps modifying LAPACK code from NETLIB.
Call Number: QA184 .D455 1997ISBN: 0898713897Publication Date: 1997-01-01
Differential Equations and Linear Algebra by
This text covers the core concepts and techniques of elementary linear algebra - matrices and linear systems, vector spaces, eigensystems and matrix exponentials - that are needed for an introduction to differential equations. The book emphasizes mathematical modelling of real-world phenomena.
Call Number: QA372 .E34 2000ISBN: 0139737510Publication Date: 2000-07-11
Differential Equations and Linear Algebra by
Written by a mathematician/engineer/scientist author who brings all three perspectives to the book. This volume offers an extremely easy-to-read and easy-to-comprehend exploration of both ordinary differential equations and linear algebra--motivated throughout by high-quality applications to science and engineering. Features many optional sections and subsections that allow topics to be covered comprehensively, moderately, or minimally, and includes supplemental coverage of Maple at the end of most sections. For anyone interested in Differential Equations and Linear Algebra.
Call Number: QA184 .G72 2001ISBN: 013011118XPublication Date: 2000-12-05
Elementary Linear Algebra by
Suitable for a sophomore-level course in Linear Algebra and based on the recommendations of the LACSG, this book focuses on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, and orthogonality. It provides a coverage of vector spaces.
Call Number: QA184 .S68 2000ISBN: 0137167229Publication Date: 1999-09-07
Elementary Linear Algebra by
Noted for its expository style and clarity of presentation, the revision of this best-selling Linear Algebra text combines Linear Algebra theory with applications, and addresses a new generation of students' changing needs.
Call Number: QA184 .A57 2000ISBN: 0471170526Publication Date: 2000-01-11
Elements of Linear Algebra by
This volume presents a thorough discussion of systems of linear equations and their solutions. Vectors and matrices are introduced as required and an account of determinants is given. Great emphasis has been placed on keeping the presentation as simple as possible, with many illustrative examples. While all mathematical assertions are proved, the student is led to view the mathematical content intuitively, as an aid to understanding. The text treats the coordinate geometry of lines, planes and quadrics, provides a natural application for linear algebra and at the same time furnished a geometrical interpretation to illustrate the algebraic concepts.
Call Number: QA251 .C63 1994ISBN: 0412552809Publication Date: 1994-07-01
Vector Calculus, Linear Algebra and Differential Forms by
This text covers most of the standard topics in multivariate calculus and a substantial part of a standard first course in linear algebra. Appendix material on harder proofs and programs allows the book to be used as a text for a course in analysis. The organization and selection of material present
Call Number: QA303.2 .H83 2002ISBN: 0130414085Publication Date: 2001-09-07
Handbook of Linear Algebra by
The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts. Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical problems.
Call Number: QA184.2 .H36 2007ISBN: 1584885106Publication Date: 2006-11-02
Applied Linear Algebra and Matrix Analysis by
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.
Call Number: QA184.2 .S56 2007ISBN: 9780387331942Publication Date: 2006-12-06
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