Linear Algebra, Geometry and Transformation

Vectors, Mappings and Linearity Numeric Vectors Functions Mappings and Transformations Linearity The Matrix of a Linear Transformation Solving Linear Systems The Linear System The Augmented Matrix and RRE Form Homogeneous Systems in RRE Form Inhomogeneous Systems in RRE Form The Gauss-Jordan Algorithm Two Mapping Answers Linear Geometry Geometric Vectors Geometric/Numeric Duality Dot-Product Geometry Lines, Planes, and Hyperplanes System Geometry and Row/Column Duality The Algebra of Matrices Matrix Operations Special Matrices Matrix Inversion A Logical Digression The Logic of the Inversion Algorithm Determinants Subspaces Basic Examples and Definitions Spans and Perps Nullspace Column-Space Perp/Span Conversion Independence Basis Dimension and Rank Orthogonality Orthocomplements Four Subspaces, 16 Questions Orthonormal Bases The Gram-Schmidt Algorithm Linear Transformation Kernel and Image The Linear Rank Theorem Eigenspaces Eigenvalues and Eigenspaces: Calculation Eigenvalues and Eigenspaces: Similarity Diagonalizability and the Spectral Theorem Singular Value Decomposition Appendix A: Determinants Appendix B: Proof of the Spectral Theorem Appendix C: Lexicon Index