Elementary linear algebra : applications version

Elementary Linear Algebra: Applications Version, 12th Edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus. Cover......Page 1 Title Page......Page 5 Copyright......Page 6 About the Authors......Page 8 Preface......Page 9 Contents......Page 13 1: Systems of Linear Equations and Matrices......Page 15 1.1 Introduction to Systems of Linear Equations......Page 16 1.2 Gaussian Elimination......Page 25 1.3 Matrices and Matrix Operations......Page 39 1.4 Inverses; Algebraic Properties of Matrices......Page 54 1.5 Elementary Matrices and a Method for Finding A-1......Page 67 1.6 More on Linear Systems and Invertible Matrices......Page 76 1.7 Diagonal, Triangular, and Symmetric Matrices......Page 83 1.8 Introduction to Linear Transformations......Page 90 1.9 Compositions of Matrix Transformations......Page 104 Network Analysis......Page 112 Electrical Circuits......Page 114 Balancing Chemical Equations......Page 117 Polynomial Interpolation......Page 119 1.11 Leontief Input-Output Models......Page 124 2.1 Determinants by Cofactor Expansion......Page 132 2.2 Evaluating Determinants by Row Reduction......Page 140 2.3 Properties of Determinants; Cramer's Rule......Page 147 3.1 Vectors in 2-Space, 3-Space, and n-Space......Page 160 3.2 Norm, Dot Product, and Distance in Rn......Page 172 3.3 Orthogonality......Page 186 3.4 The Geometry of Linear Systems......Page 197 3.5 Cross Product......Page 204 4.1 Real Vector Spaces......Page 216 4.2 Subspaces......Page 225 4.3 Spanning Sets......Page 234 4.4 Linear Independence......Page 242 4.5 Coordinates and Basis......Page 252 4.6 Dimension......Page 262 4.7 Change of Basis......Page 270 4.8 Row Space, Column Space, and Null Space......Page 277 4.9 Rank, Nullity, and the Fundamental Matrix Spaces......Page 290 5.1 Eigenvalues and Eigenvectors......Page 305 5.2 Diagonalization......Page 315 5.3 Complex Vector Spaces......Page 325 5.4 Differential Equations......Page 337 5.5 Dynamical Systems and Markov Chains......Page 343 6.1 Inner Products......Page 355 6.2 Angle and Orthogonality in Inner Product Spaces......Page 366 6.3 Gram–Schmidt Process; QR-Decomposition......Page 375 6.4 Best Approximation; Least Squares......Page 390 6.5 Mathematical Modeling Using Least Squares......Page 399 6.6 Function Approximation; Fourier Series......Page 406 7.1 Orthogonal Matrices......Page 413 7.2 Orthogonal Diagonalization......Page 422 7.3 Quadratic Forms......Page 430 7.4 Optimization Using Quadratic Forms......Page 443 7.5 Hermitian, Unitary, and Normal Matrices......Page 450 8.1 General Linear Transformations......Page 460 8.2 Compositions and Inverse Transformations......Page 473 8.3 Isomorphism......Page 485 8.4 Matrices for General Linear Transformations......Page 491 8.5 Similarity......Page 501 8.6 Geometry of Matrix Operators......Page 507 9.1 LU-Decompositions......Page 523 9.2 The Power Method......Page 533 9.3 Comparison of Procedures for Solving Linear Systems......Page 542 9.4 Singular Value Decomposition......Page 546 9.5 Data Compression Using Singular Value Decomposition......Page 554 10: Applications of Linear Algebra......Page 559 10.1 Constructing Curves and Surfaces Through Specified Points......Page 560 10.2 The Earliest Applications of Linear Algebra......Page 565 10.3 Cubic Spline Interpolation......Page 572 10.4 Markov Chains......Page 582 10.5 Graph Theory......Page 591 10.6 Games of Strategy......Page 601 10.7 Forest Management......Page 609 10.8 Computer Graphics......Page 616 10.9 Equilibrium Temperature Distributions......Page 624 10.10 Computed Tomography......Page 633 10.11 Fractals......Page 643 10.12 Chaos......Page 659 10.13 Cryptography......Page 672 10.14 Genetics......Page 683 10.15 Age-Specific Population Growth......Page 692 10.16 Harvesting of Animal Populations......Page 701 10.17 A Least Squares Model for Human Hearing......Page 709 10.18 Warps and Morphs......Page 715 10.19 Internet Search Engines......Page 724 10.20 Facial Recognition......Page 730 APPENDIX A: Working with Proofs......Page 740 APPENDIX B: Complex Numbers......Page 744 Answers to Exercises......Page 752 Index......Page 791 Applications and Historical Topics......Page 801 EULA......Page 803 Elementary Linear Algebra: Applications Version, 12th Edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus