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| Elementary Linear Algebra With Applications 10th Edition | |
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| Systems Of Linear Equations And Matrices | |
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| Introduction to Systems of Linear Equations | |
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| Gaussian Elimination | |
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| Matrices and Matrix Operations | |
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| Inverses Algebraic Properties of Matrices | |
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| Elementary Matrices and a Method for Finding A-1 | |
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| More on Linear Systems and Invertible Matrices | |
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| Diagonal, Triangular, and Symmetric Matrices | |
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| Applications of Linear Systems (Traffic flow Electrical Networks Balancing Chemical Equations, Polynomial Interpolation | |
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| Leontief Input-Output Models Chapter Summary | |
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| Determinants | |
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| Determinants by Cofactor Expansion | |
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| Evaluating Determinants by Row Reduction | |
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| Properties of Determinants Adjoint Crame's Rule Chapter Summary | |
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| Euclidean Vector Spaces | |
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| Vectors in 2-space, 3-space, and n-space | |
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| Norm, Dot Product, and Distance in Rn | |
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| Orthogonality | |
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| The Geometry of Linear Systems | |
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| Cross Product Chapter Summary | |
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| General Vector Spaces | |
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| Real Vector Spaces | |
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| Subspaces | |
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| Linear Independence | |
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| Coordinates and Basis | |
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| Dimension | |
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| Change of Basis | |
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| Row Space, Column Space, and Null Space | |
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| Rank, Nullity, and the Fundamental Matrix Spaces | |
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| Linear Transformations from Rn to Rm | |
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| Properties of Matrix Transformations from Rn to Rm | |
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| Geometry of Matrix Operators | |
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| Dynamical Systems and Markov Chains Chapter Summary | |
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| Eignvalues And Eigenvectors | |
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| Eigenvalues and Eigenvectors | |
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| Diagonalization | |
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| Complex Vector Spaces | |
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| Application to Differential Equations Chapter Summary | |
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| Inner Product Spaces | |
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| Inner Products | |
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| Angle and Orthogonality in Inner Product Spaces | |
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| Orthonormal Bases Gram-Schmidt Process QR - Decomposition | |
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| Best Approximation Least Squares | |
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| Least Squares Fitting to Data | |
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| Fourier Series Chapter Summary | |
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| Diagonalization And Quadratic Forms | |
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| Orthogonal Matrices | |
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| Orthogonal Diagonalization | |
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| Quadratic Forms | |
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| Application of Quadratic Forms to Optimization | |
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| Hermitian, Unitary, and Normal Matrices Chapter Summary | |
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| Linear Transformations | |
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| General Linear Transformations | |
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| Isomorphism | |
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| Composition and Inverse Transformations | |
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| Matrices of General Linear Transformations | |
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| Similarity Chapter Summary | |
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| Numerical Methods | |
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| Matrix Factorization and LU-Decompositions | |
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| The Power Method | |
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| Application to Internet Search Engines | |
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| Comparison of Procedures for Solving Linear Systems | |
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| Singular-Value Decomposition | |
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| Application of Singular Value Decomposition to Data Compression Chapter Summary | |
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| Applications Of Linear Algebra | |
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| Constructing Curves and Surfaces through Specified Points | |
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| Geometric Linear Programming | |
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| The Earliest Applications of Linear Algebra | |
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| Cubic Spline Interpolation | |
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| Graph Theory | |
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| Games of Strategy | |
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| Forest Management | |
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| Equilibrium Temperature Distributions | |
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| Computed Tomography | |
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| Fractals | |
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| Chaos | |
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| Cryptography | |
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| Genetics | |
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| Age-Specific Population Growth | |
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| Harvesting of Animal Populations | |
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| A Least Squares Model for Human Hearing | |
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| Warps and Morphs | |
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| How to Read Theorems | |
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| Complex Numbers | |