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Produktbild: Elementary Linear Algebra, 12th Edition Internatio nal Adaptation, Revised and Updated

Elementary Linear Algebra, 12th Edition Internatio nal Adaptation, Revised and Updated

Fr. 112.00

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

11.09.2025

Verlag

WILEY

Seitenzahl

816

Maße (L/B/H)

27.3/21.4/3.4 cm

Gewicht

1718 g

Auflage

12. Auflage

Sprache

Englisch

ISBN

978-1-394-37872-2

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

11.09.2025

Verlag

WILEY

Seitenzahl

816

Maße (L/B/H)

27.3/21.4/3.4 cm

Gewicht

1718 g

Auflage

12. Auflage

Sprache

Englisch

ISBN

978-1-394-37872-2

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Elementary Linear Algebra, 12th Edition Internatio nal Adaptation, Revised and Updated

  • 1 Systems of Linear Equations and Matrices 1

    1.1 Introduction to Systems of Linear Equations 2

    1.2 Gaussian Elimination 11

    1.3 Matrices and Matrix Operations 25

    1.4 Inverses; Algebraic Properties of Matrices 40

    1.5 Elementary Matrices and a Method for Finding A - 1 53

    1.6 More on Linear Systems and Invertible Matrices 62

    1.7 Diagonal, Triangular, and Symmetric Matrices 69

    1.8 Introduction to Linear Transformations 76

    1.9 Compositions of Matrix Transformations 90

    1.10 Applications of Linear Systems 98

    Network Analysis 98

    Electrical Circuits 100

    Balancing Chemical Equations 103

    Polynomial Interpolation 105

    1.11 Leontief Input-Output Models 110

    2 Determinants 119

    2.1 Determinants by Cofactor Expansion 119

    2.2 Evaluating Determinants by Row Reduction 127

    2.3 Properties of Determinants; Cramer's Rule 134

    3 Euclidean Vector Spaces 149

    3.1 Vectors in 2-Space, 3-Space, and n-Space 149

    3.2 Norm, Dot Product, and Distance in R n 161

    3.3 Orthogonality 175

    3.4 The Geometry of Linear Systems 186

    3.5 Cross Product 193

    4 General Vector Spaces 205

    4.1 Real Vector Spaces 205

    4.2 Subspaces 214

    4.3 Spanning Sets 223

    4.4 Linear Independence 231

    4.5 Coordinates and Basis 241

    4.6 Dimension 251

    4.7 Change of Basis 259

    4.8 Row Space, Column Space, and Null Space 266

    4.9 Rank, Nullity, and the Fundamental Matrix Spaces 279

    5 Eigenvalues and Eigenvectors 295

    5.1 Eigenvalues and Eigenvectors 295

    5.2 Diagonalization 305

    5.3 Complex Vector Spaces 315

    5.4 Differential Equations 327

    5.5 Dynamical Systems and Markov Chains 333

    6 Inner Product Spaces 347

    6.1 Inner Products 347

    6.2 Angle and Orthogonality in Inner Product Spaces 358

    6.3 Gram-Schmidt Process; QR-Decomposition 367

    6.4 Best Approximation; Least Squares 382

    6.5 Mathematical Modeling Using Least Squares 391

    6.6 Function Approximation; Fourier Series 398

    7 Diagonalization and Quadratic Forms 407

    7.1 Orthogonal Matrices 407

    7.2 Orthogonal Diagonalization 416

    7.3 Quadratic Forms 424

    7.4 Optimization Using Quadratic Forms 437

    7.5 Hermitian, Unitary, and Normal Matrices 444

    8 General Linear Transformations 455

    8.1 General Linear Transformations 455

    8.2 Compositions and Inverse Transformations 468

    8.3 Isomorphism 480

    8.4 Matrices for General Linear Transformations 486

    8.5 Similarity 496

    8.6 Geometry of Matrix Operators 502

    9 Numerical Methods 519

    9.1 LU-Decompositions 519

    9.2 The Power Method 529

    9.3 Comparison of Procedures for Solving Linear Systems 538

    9.4 Singular Value Decomposition 542

    9.5 Data Compression Using Singular Value Decomposition 550

    10 Applications of Linear Algebra 555

    10.1 Constructing Curves and Surfaces Through Specified Points 555

    10.2 The Earliest Applications of Linear Algebra 561

    10.3 Cubic Spline Interpolation 568

    10.4 Markov Chains 578

    10.5 Graph Theory 587

    10.6 Games of Strategy 597

    10.7 Forest Management 605

    10.8 Computer Graphics 612

    10.9 Equilibrium Temperature Distributions 620

    10.10 Computed Tomography 629

    10.11 Fractals 639

    10.12 Chaos 655

    10.13 Cryptography 668

    10.14 Genetics 679

    10.15 Age-Specific Population Growth 688

    10.16 Harvesting of Animal Populations 697

    10.17 A Least Squares Model for Human Hearing 705

    10.18 Warps and Morphs 711

    10.19 Internet Search Engines 720

    10.20 Facial Recognition 726

    Appendix A Working with Proofs A1

    Appendix B Complex Numbers A7

    Answers to Exercises A15

    Index i1