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Linear Algebra and Its Applications by David C. Lay (2002, Hardcover)

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Product Identifiers

PublisherAddison-Wesley Longman, Incorporated

ISBN-100201709708

ISBN-139780201709704

eBay Product ID (ePID)2397962

Product Key Features

Number of Pages576 Pages

LanguageEnglish

Publication NameLinear Algebra and Its Applications

SubjectAlgebra / Linear, Algebra / General

Publication Year2002

TypeTextbook

AuthorDavid C. Lay

Subject AreaMathematics

FormatHardcover

Dimensions

Item Height0.9 in

Item Weight40.4 Oz

Item Length9.4 in

Item Width8.3 in

Additional Product Features

Edition Number3

Intended AudienceCollege Audience

LCCN2002-019102

Dewey Edition23

IllustratedYes

Dewey Decimal512.5

Table Of Content( Supplementary Exercises are featured at the end of each chapter. ) 1. Linear Equations in Linear Algebra. Introductory Example: Linear Models in Economics and Engineering.Systems of Linear Equations.Row Reduction and Echelon Forms.Vector Equations.The Matrix Equation A x = b .Solution Sets of Linear Systems.Applications of Linear Systems.Linear Independence.Introduction to Linear Transformations.The Matrix of a Linear Transformation.Linear Models in Business, Science, and Engineering. 2. Matrix Algebra. Introductory Example: Computer Graphics in Aircraft Design.Matrix Operations.The Inverse of a Matrix.Characterizations of Invertible Matrices.Partitioned Matrices.Matrix Factorizations.The Leontief Input-Output Model.Applications to Computer Graphics.Subspaces of Rn.Dimensions and Rank. 3. Determinants. Introductory Example: Determinants in Analytic Geometry.Introduction to Determinainants.Properties of Determinants.Cramer's Rule, Volume, and Linear Transformations. 4. Vector Spaces. Introductory Example: Space Flight and Control Systems.Vector Spaces and Subspaces.Null Spaces, Column Spaces, and Linear Transformations.Linearly Independent Sets; Bases.Coordinate Systems.The Dimension of Vector SpaceRank.Change of Basis.Applications to Difference Equations.Applications to Markov Chains. 5. Eigenvalues and Eigenvectors. Introductory Example: Dynamical Systems and Spotted Owls.Eigenvectors and Eigenvalues.The Characteristic Equation.Diagonalization.Eigenvectors and Linear Transformations.Complex Eigenvalues.Discrete Dynamical Systems.Applications to Differential Equations.Iterative Estimates for Eigenvalues. 6. Orthogonality and Least-Squares. Introductory Example: Readjusting the North American Datum.Inner Product, Length, and Orthogonality.Orthogonal Sets.Orthogonal Projections.The Gram-Schmidt Process.Least-Squares Problems.Applications to Linear Models.Inner Product Spaces.Applications of Inner Product Spaces. 7. Symmetric Matrices and Quadratic Forms. Introductory Example: Multichannel Image Processing.Diagonalization of Symmetric Matrices.Quadratic Forms.Constrained Optimization.The Singular Value Decomposition.Applications to Image Processing and Statistics.Appendices. A. Uniqueness of the Reduced Echelon Form.B. Complex NumbersGlossary.Answers.Index.

SynopsisLinear 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. - New full color design allows for clearer understanding of figures and graphically important concepts and procedures. - MyMathLab is now available, integrating the texts content with the Student Study Guide. All of the texts many electronic resources can be found on MyMathLab. - MathXL is now available for the text, allowing students to take tests and quizzes online. - An electronic test generato, 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.

LC Classification NumberQA184.2.L39 2003