Elementary Linear Algebra

Hardcover | June 23, 2008

byStewart Venit, Wayne Bishop, Jason Brown

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Elementary Linear Algebra, First Canadian Edition, features a computational emphasis and contains just the right mix of theory and worked examples. The authors provide students with easy-to-read explanations, examples, proofs and procedures and also stress that linear algebra has many interesting and important applications, both in the sciences and the arts.The book mixes the theory and practice of linear algebra seamlessly, with a variety of interesting and topical applications such as music and fractals throughout, including one section that deals with using Fourier transforms to uncover the secrets behind the opening chords of a song!

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Elementary Linear Algebra, First Canadian Edition, features a computational emphasis and contains just the right mix of theory and worked examples. The authors provide students with easy-to-read explanations, examples, proofs and procedures and also stress that linear algebra has many interesting and important applications, both in th...

Format:HardcoverDimensions:528 pages, 11.19 × 8.94 × 0.94 inPublished:June 23, 2008Publisher:Nelson College IndigenousLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0176440763

ISBN - 13:9780176440763

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Table of Contents

Chapter 1: Geometry of R2 and R31.1 Vectors in R2 and R31.2 Dot and Cross Products1.3 Lines and PlanesApplication 1?Vectors and InteractiveMultimediaChapter SummaryKeywordsSelf-TestReview ExercisesChallenge YourselfChapter 2: Euclidean m-Space and Linear Equations2.1 Euclidean m-Space2.2 Systems of Linear Equations2.3 Row-Reduction of Linear SystemsApplication 1?ElectricalCircuitsand Pipe NetworksApplication 2?Interpolating PolynomialsChapter SummaryKeywordsSelf-TestReview ExercisesChallenge Yourself Chapter 3: Matrices3.1 Operations on Matrices3.2 Matrix equations and Inverses 3.3 Theory of Linear Systems 3.4 LU Decomposition 3.5 Elementary Matrices and Linear Systems Application 1?Least Square PolynomialsApplication 2?Input-Output Analysis: Leontief ModelsChapter SummaryKeywordsSelf-TestReview ExercisesChallenge YourselfChapter 4: Determinants4.1 Definition of Determinant4.2 Properties of Determinants4.3 Cramers Rule4.4 An Introduction to EigenvaluesApplication 1?Markov ChainsChapter SummaryKeywordsSelf-TestReview ExercisesChallenge YourselfChapter 5: Independence and Basis in Rm 5.1 Linear dependence and Independence5.2 Subspaces of Rm5.3 Basis and Dimension5.4 Rank of a MatrixApplication 1?Signal CompressionChapter SummaryKeywordsSelf-TestReview ExercisesChallenge YourselfChapter 6: Vector Spaces6.1 Vector Spaces and Subspaces6.2 Linear Independence, Basis, and Dimension6.3 Coordinate Vectors6.4 Inner product Spaces6.5 Vector Spaces over Other FieldsApplication 1?Approximation of Continuous Functions; Fourier SeriesApplication 2?Music, Fourier Transforms, and A Hard Days NightApplication 3?Fractals I: Self SimilarityProjections and Seeds Chapter SummaryKeywordsSelf-Test Review Exercises Challenge Yourself Chapter 7: Linear Transformations 7.1 Definition of a Linear Transformation 7.2 Algebra of Linear Transformations 7.3 Kernel and Image 7.4 Matrix of a General Linear Transformation 7.5 Change of Basis Application 1?linear Differential equations Application 2?Fractals II: Contractive Affine Maps and IFSsChapter Summary Keywords Self-Test Review Exercises Challenge Yourself Chapter 8: Eigenvalues and Eigenvectors 8.1 Definitions and Examples 8.2 Diagonalization 8.3 The QR Method for Approximating Eigenvalues 8.4 Complex Eigenvalues and Eigenvectors Application 1?Quadric Surfaces Application 2? Fractals III: When is an Affine Map Contractive? Chapter Summary Keywords Self-Test Review Exercises Challenge Yourself Chapter 9: Linear Programming 9.1 Introduction and Terminology 9.2 The Simplex Algorithm 9.3 Nonstandard LP Problems 9.4 Theory of Linear Programming Application 1?Supply and Demand Chapter Summary Keywords Self-Test Review Exercises Challenge Yourself APPENDIXES Appendix A A Short Introduction to MAPLE Appendix B Answers to Self Test Problems Answers to Odd-Numbered Exercises Index