Last updated 12:25 AM, March 9, 2004.
Lecture Notes
| Linear Algebra Notes full notes (436KB) | |
| Title Page and Contents | |
| Linear Systems | |
| Systems of Linear Equations | |
| Gauss-Jordan Elimination | |
| Examples, in text format | |
| The Z_p Fields | |
| Systems of Linear Equations in Z_p | |
| Matrix Algebra | |
| Matrix Arithmetic | |
| Elementary Matrices | |
| Matrix Inverse | |
| Method for Finding the Inverse | |
| Diagonal, Triangular and Symmetric Matrices | |
| Determinant | |
| The Determinant Function | |
| Calculating the Determinant for 2-by-2 Matrices | |
| Geometric Meaning of the Determinant | |
| Properties of the Determinant Function | |
| Evaluating the Determinant by Row Reduction | |
| Determinant, Invertibility and Systems of Linear Equations | |
| Cofactor Expansion, Adjoint Matrix | |
| Calculating the Determinant for 3-by-3 Matrices | |
| Block-Triangular Matrices | |
| Vector Spaces | |
| Introduction to the Euclidean n-space | |
| Linear Transformation from R^n to R^m | |
| Real Vector Spaces | |
| Subspaces | |
| Spanning | |
| Linear Independence | |
| Basis and Dimension | |
| Column Space, Row Space, Null Space, Rank and Nullity | |
| Eigenvalues and Eigenvectors | |
| Eigenvalues and Eigenvectors | |
| Examples | |
| Diagonalization | |
| Computing Powers of a Matrix | |
| General Linear Transformations | |
| Linear Transformations | |
| General Linear Transformations | |
| Matrix Representations of Linear Transformations | |
| Kernel and Range of Linear Transformations | |
| Supplementary Material | |
| Cayley-Hamilton Theorem | |
| Exponential of Matrices | |
| Laplace Expansion for Determinant | |
| First Minors and Cofactors | |
| Alien Cofactors | |
| Cramer's Formula | |
| Appendix C | |
| Rules of Matrix Arithmetic | |
| Equivalent Statements | |
| Index | |