لایب سان

Cover -- Title Page -- Copyright -- About the Authors -- Preface -- Contents -- 1: Systems of Linear Equations and Matrices -- 1.1 Introduction to Systems of Linear Equations -- 1.2 Gaussian Elimination -- 1.3 Matrices and Matrix Operations -- 1.4 Inverses -- Algebraic Properties of Matrices -- 1.5 Elementary Matrices and a Method for Finding A-1 -- 1.6 More on Linear Systems and Invertible Matrices -- 1.7 Diagonal, Triangular, and Symmetric Matrices -- 1.8 Introduction to Linear Transformations -- 1.9 Compositions of Matrix Transformations -- 1.10 Applications of Linear Systems Network Analysis -- Electrical Circuits -- Balancing Chemical Equations -- Polynomial Interpolation -- 1.11 Leontief Input-Output Models -- 2: Determinants -- 2.1 Determinants by Cofactor Expansion -- 2.2 Evaluating Determinants by Row Reduction -- 2.3 Properties of Determinants -- Cramer's Rule -- 3: Euclidean Vector Spaces -- 3.1 Vectors in 2-Space, 3-Space, and n-Space -- 3.2 Norm, Dot Product, and Distance in Rn -- 3.3 Orthogonality -- 3.4 The Geometry of Linear Systems -- 3.5 Cross Product -- 4: General Vector Spaces -- 4.1 Real Vector Spaces -- 4.2 Subspaces -- 4.3 Spanning Sets 4.4 Linear Independence -- 4.5 Coordinates and Basis -- 4.6 Dimension -- 4.7 Change of Basis -- 4.8 Row Space, Column Space, and Null Space -- 4.9 Rank, Nullity, and the Fundamental Matrix Spaces -- 5: Eigenvalues and Eigenvectors -- 5.1 Eigenvalues and Eigenvectors -- 5.2 Diagonalization -- 5.3 Complex Vector Spaces -- 5.4 Differential Equations -- 5.5 Dynamical Systems and Markov Chains -- 6: Inner Product Spaces -- 6.1 Inner Products -- 6.2 Angle and Orthogonality in Inner Product Spaces -- 6.3 Gram-Schmidt Process -- QR-Decomposition -- 6.4 Best Approximation -- Least Squares 6.5 Mathematical Modeling Using Least Squares -- 6.6 Function Approximation -- Fourier Series -- 7: Diagonalization and Quadratic Forms -- 7.1 Orthogonal Matrices -- 7.2 Orthogonal Diagonalization -- 7.3 Quadratic Forms -- 7.4 Optimization Using Quadratic Forms -- 7.5 Hermitian, Unitary, and Normal Matrices -- 8: General Linear Transformations -- 8.1 General Linear Transformations -- 8.2 Compositions and Inverse Transformations -- 8.3 Isomorphism -- 8.4 Matrices for General Linear Transformations -- 8.5 Similarity -- 8.6 Geometry of Matrix Operators -- 9: Numerical Methods 9.1 LU-Decompositions -- 9.2 The Power Method -- 9.3 Comparison of Procedures for Solving Linear Systems -- 9.4 Singular Value Decomposition -- 9.5 Data Compression Using Singular Value Decomposition -- 10: Applications of Linear Algebra -- 10.1 Constructing Curves and Surfaces Through Specified Points -- 10.2 The Earliest Applications of Linear Algebra -- 10.3 Cubic Spline Interpolation -- 10.4 Markov Chains -- 10.5 Graph Theory -- 10.6 Games of Strategy -- 10.7 Forest Management -- 10.8 Computer Graphics -- 10.9 Equilibrium Temperature Distributions -- 10.10 Computed Tomography

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