Textbook in PDF format About the Authors Licensing Overview Systems of Linear Equations- Algebra Systems of Linear Equations Row Reduction Parametric Form Systems of Linear Equations- Geometry Vectors Vector Equations and Spans Matrix Equations Solution Sets Linear Independence Subspaces Basis and Dimension The Rank Theorem Bases as Coordinate Systems Linear Transformations and Matrix Algebra Prelude to Linear Transformations and Matrix Algebra Matrix Transformations One-to-one and Onto Transformations Linear Transformations Matrix Multiplication Matrix Inverses The Invertible Matrix Theorem Determinants Determinants- Definition Cofactor Expansions Determinants and Volumes Eigenvalues and Eigenvectors Eigenvalues and Eigenvectors The Characteristic Polynomial Diagonalization Complex Eigenvalues Stochastic Matrices Similarity Orthogonality Dot Products and Orthogonality Orthogonal Complements Orthogonal Projection Orthogonal Sets The Method of Least Squares Appendix A - Complex Numbers B - Notation C - Hints and Solutions to Selected Exercises Index Glossary D- GNU Free Documentation License Index Detailed Licensing