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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