"Starting with all the standard topics of a first course in linear algebra, this text then introduces linear mappings, and the questions they raise, with the expectation of resolving those questions throughout the book. Ultimately, by providing an emphasis on developing computational and conceptual skills, students are elevated from the computational mathematics that often dominates their experience prior to the course to the conceptual reasoning that often dominates at the conclusion"-- Read more...
Abstract: "Starting with all the standard topics of a first course in linear algebra, this text then introduces linear mappings, and the questions they raise, with the expectation of resolving those questions throughout the book. Ultimately, by providing an emphasis on developing computational and conceptual skills, students are elevated from the computational mathematics that often dominates their experience prior to the course to the conceptual reasoning that often dominates at the conclusion"
Content: Vectors, Mappings and Linearity Numeric Vectors Functions Mappings and Transformations Linearity The Matrix of a Linear Transformation Solving Linear Systems The Linear SystemThe 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 DecompositionAppendix A: Determinants Appendix B: Proof of the Spectral TheoremAppendix C: Lexicon Index
