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Linear Algebra and Its Applications 6th EDITION (Global Edition) 요약정보 및 구매

상품 선택옵션 0 개, 추가옵션 0 개

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지은이 David C. Lay, Steven R. Lay, Judi J. McDonald
발행년도 2021-07-06
판수 6판
페이지 672
ISBN 9781292351216
도서상태 구매가능
판매가격 53,000원
포인트 0점
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  • Linear Algebra and Its Applications 6th EDITION (Global Edition)
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관련상품

  • Fosters the concepts and skills needed for future careers

    Linear Algebra and Its Applications offers a modern elementary introduction with broad, relevant applications. With traditional texts, the early stages of the course are relatively easy as material is presented in a familiar, concrete setting, but students often hit a wall when abstract concepts are introduced. Certain concepts fundamental to the study of linear algebra (such as linear independence, vector space, and linear transformations) require time to assimilate and students' understanding of them is vital.

    Lay, Lay, and McDonald make these concepts more accessible by introducing them early in a familiar, concrete setting, developing them gradually, and returning to them throughout the text so that students can grasp them when they are discussed in the abstract. The 6th Edition offers exciting new material, examples, and online resources, along with new topics, vignettes, and applications.

  • 1. Linear Equations in LinearAlgebra

    Introductory Example: LinearModels in Economics and Engineering

    1.1 Systems of Linear Equations

    1.2 Row Reduction and EchelonForms

    1.3 Vector Equations

    1.4 The Matrix Equation Ax= b

    1.5 Solution Sets of LinearSystems

    1.6 Applications of Linear Systems

    1.7 Linear Independence

    1.8 Introduction to LinearTransformations

    1.9 The Matrix of a LinearTransformation

    1.10 Linear Models in Business,Science, and Engineering

    Projects

    Supplementary Exercises

     

    2. Matrix Algebra

    Introductory Example: ComputerModels in Aircraft Design

    2.1 Matrix Operations

    2.2 The Inverse of a Matrix

    2.3 Characterizations ofInvertible Matrices

    2.4 Partitioned Matrices

    2.5 Matrix Factorizations

    2.6 The Leontief InputOutputModel

    2.7 Applications to ComputerGraphics

    2.8 Subspaces of n

    2.9 Dimension and Rank

    Projects

    Supplementary Exercises

     

    3. Determinants

    Introductory Example: Random Pathsand Distortion

    3.1 Introduction to Determinants

    3.2 Properties of Determinants

    3.3 Cramers Rule, Volume, andLinear Transformations

    Projects

    Supplementary Exercises

     

    4. Vector Spaces

    Introductory Example: Space Flightand Control Systems

    4.1 Vector Spaces and Subspaces

    4.2 Null Spaces, Column Spaces,and Linear Transformations

    4.3 Linearly Independent Sets;Bases

    4.4 Coordinate Systems

    4.5 The Dimension of a VectorSpace

    4.6 Change of Basis

    4.7 Digital Signal Processing

    4.8 Applications to DifferenceEquations

    Projects

    Supplementary Exercises

     

    5. Eigenvalues and Eigenvectors

    Introductory Example: DynamicalSystems and Spotted Owls

    5.1 Eigenvectors and Eigenvalues

    5.2 The Characteristic Equation

    5.3 Diagonalization

    5.4 Eigenvectors and LinearTransformations

    5.5 Complex Eigenvalues

    5.6 Discrete Dynamical Systems

    5.7 Applications to DifferentialEquations

    5.8 Iterative Estimates forEigenvalues

    5.9 Markov Chains

    Projects

    Supplementary Exercises

     

    6. Orthogonality and Least Squares

    Introductory Example: The NorthAmerican Datum and GPS Navigation

    6.1 Inner Product, Length, andOrthogonality

    6.2 Orthogonal Sets

    6.3 Orthogonal Projections

    6.4 The GramSchmidt Process

    6.5 Least-Squares Problems

    6.6 Machine Learning and LinearModels

    6.7 Inner Product Spaces

    6.8 Applications of Inner ProductSpaces

    Projects

    Supplementary Exercises

     

    7. Symmetric Matrices andQuadratic Forms

    Introductory Example: MultichannelImage Processing

    7.1 Diagonalization of SymmetricMatrices

    7.2 Quadratic Forms

    7.3 Constrained Optimization

    7.4 The Singular ValueDecomposition

    7.5 Applications to ImageProcessing and Statistics

    Projects

    Supplementary Exercises

     

    8. The Geometry of Vector Spaces

    Introductory Example: The PlatonicSolids

    8.1 Affine Combinations

    8.2 Affine Independence

    8.3 Convex Combinations

    8.4 Hyperplanes

    8.5 Polytopes

    8.6 Curves and Surfaces

    Projects

    Supplementary Exercises

     

    9. Optimization

    Introductory Example: The BerlinAirlift

    9.1 Matrix Games

    9.2 Linear ProgrammingGeometricMethod

    9.3 Linear ProgrammingSimplexMethod

    9.4 Duality

    Projects

    Supplementary Exercises

     

    10. Finite-State Markov Chains(Online Only)

    Introductory Example: GooglingMarkov Chains

    10.1 Introduction and Examples

    10.2 The Steady-State Vector andGoogle's PageRank

    10.3 Communication Classes

    10.4 Classification of States andPeriodicity

    10.5 The Fundamental Matrix

    10.6 Markov Chains and BaseballStatistics

     

    Appendices

    A. Uniqueness of the ReducedEchelon Form

    B. Complex Numbers

  • David C. Lay, University of MarylandCollege Park

    Steven R. Lay, Lee University

    Judi J. McDonald, Washington State University

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선택된 옵션

  • Linear Algebra and Its Applications 6th EDITION (Global Edition)
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