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Systems Of Linear Equations And Matrices | |
Introduction to Systems of Linear Equations | |
Gaussian Elimination | |
Matrices and Matrix Operations | |
Inverses Algebraic Properties of Matrices | |
Elementary Matrices and a Method for Finding A-1 | |
More on Linear Systems and Invertible Matrices | |
Diagonal, Triangular, and Symmetric Matrices | |
Applications of Linear Systems (Traffic flow Electrical Networks Balancing Chemical Equations, Polynomial Interpolation) | |
Leontief Input-Output Models * Chapter Summary | |
Determinants | |
Determinants by Cofactor Expansion | |
Evaluating Determinants by Row Reduction | |
Properties of Determinants Adjoint Cramer's Rule * Chapter Summary | |
Euclidean Vector Spaces | |
Vectors in 2-space, 3-space, and n-space | |
Norm, Dot Product, and Distance in Rn | |
Orthogonality | |
The Geometry of Linear Systems | |
Cross Product * Chapter Summary | |
General Vector Spaces | |
Real Vector Spaces | |
Subspaces | |
Linear Independence | |
Coordinates and Basis | |
Dimension | |
Change of Basis | |
Row Space, Column Space, and Null Space | |
Rank, Nullity, and the Fundamental Matrix Spaces | |
Linear Transformations from Rn to Rm | |
Properties of Matrix Transformations from Rn to Rm | |
Geometry of Matrix Operators | |
Dynamical Systems and Markov Chains * Chapter Summary | |
Eignvalues And Eigenvectors | |
Eigenvalues and Eigenvectors | |
Diagonalization | |
Complex Vector Spaces | |
Application to Differential Equations * Chapter Summary | |
Inner Product Spaces | |
Inner Products | |
Angle and Orthogonality in Inner Product Spaces | |
Orthonormal Bases Gram-Schmidt Process QR - Decomposition | |
Best Approximation Least Squares | |
Least Squares Fitting to Data | |
Fourier Series * Chapter Summary | |
Diagonalization And Quadratic Forms | |
Orthogonal Matrices | |
Orthogonal Diagonalization | |
Quadratic Forms | |
Application of Quadratic Forms to Optimization | |
Hermitian, Unitary, and Normal Matrices * Chapter Summary | |
Linear Transformations | |
General Linear Transformations | |
Isomorphism | |
Composition and Inverse Transformations | |
Matrices of General Linear Transformations | |
Similarity * Chapter Summary | |
Numerical Methods | |
Matrix Factorization and LU-Decompositions | |
The Power Method | |
Application to Internet Search Engines | |
Comparison of Procedures for Solving Linear Systems | |
Singular-Value Decomposition | |
Application of Singular Value Decomposition to Data Compression * Chapter Summary | |
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