Chapter 1 Linear Equations in Linear Algebra 1.1 Systems of Linear Equations 1.2 Row Reduction and Echelon Forms 1.3 Solutions of Linear Systems 1.4 Vector Equations Exercises Chapter 2 Matrix Algebra 2.1 Matrix Operations 2.2 The Inverse of a Matrix 2.3 Partitoned Matrices 2.4 Matrix Factorizations 2.5 Subspace of Rn 2.6 Dimension and Rank Exercises Chapter 3 Determinants 3.1 Introduction to Determinants 3.2 Properties of Determinants 3.3 Cofactor Expansion 3.4 The Inverse of a Matrix 3.5 Cramer's Rule Exercises Chapter 4 Vector Spaces 4.1 Definition of Vector Spaces 4.2 Subspaces and Span 4.3 Linearly Independent Sets 4.4 Bases and Dimension 4.5 Inner Product, Length, Angle 4.6 Orthonormal Basis and the Gram-Schmidt Procedure Exercises Chapter 5 Eigenvalues and Eigenvectors 5.1 Definition of Eigenvalues and Eigenvectors 5.2 Properties of Eigenvalues and Eigenvectors 5.3 Similarity and Diagonalization 5.4 Diagonalization of Symmetric Matrices Exercises Chapter 6 Solution Sets of Linear Systems 6.1 Homogeneous Linear Systems 6.2 Solutions of Nonhomogeneous Systems 6.3 Applications of Linear Systems Exercises Chapter 7 Symmetric Matrices and Quadratic Forms 7.1 Diagonalization of Symmetric Matrices 7.2 Quadratic Forms 7.3 Quadratic Problems 7.4 The Singular Value Decomposition 7.5 Applications to Statistics Exercises References
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