Elementary Linear Algebra

Chapter 1 Linear Equations and Matrices 1.1 Matrices 1.2 Linear Equations 1.3 Homogeneous Systems 1.4 Matrix Multiplication 1.5 Matrix Inverses 1.6 Elementary Matrices 1.7 Lu-Factorization 1.8 Application ot Markov Chains Chapter 2 Determinants and Eigenvalues 2.1 Cofactor Expansions 2.2 Determinants and Inversees 2.3 Diagonalization and Eigenvalues 2.4 Linear Dynamical Systems 2.5 Complex Eignevalues 2.6 Linear Recurrences 2.7 Polynomial Interpolation 2.8 Systems of Differential Equations Chapter 3 Vector Geometry 3.1 Geometric Vectors 3.2 Dot Product and Projections 3.3 Lines and Planes 3.4 Matrix Transformation of R^2 3.5 The Cross Product: Optional Chapter 4 The Vector Space R^n 4.1 Subspaces and Spanning 4.2 Linear Independence 4.3 Dimension 4.4 Rank 4.5 Orthogonality 4.6 Projections and Approximation 4.7 Orthogonal Diagonalization 4.8 Quadratic Forms 4.9 Linear Transformations 4.10 Complex Matrices 4.11 Singular Value Decomposition Chapter 5 Vector Spaces 5.1 Examples and Basic Properties 5.2 Independence and Dimension 5.3 Linear Transformations 5.4 Isomorphisms and Matrices 5.5 Linear Operations and Similarity 5.6 Invariant Subspaces 5.7 General Inner Products Appendix A.1 Basic Trigonometry A.2 Induction A.3 Polynomials