Course Outline:

Vector Spaces Definitions and Examples Subspaces Linear Independence Bases and Finite-Dimensional Vector Spaces Important Theorems Linear Transformations Definitions and Examples Kernal and Image Useful Theorems Isomorphism Matrix Representation Systems of Linear Equations Definition and Basics Gauss-Jordan Elimination Applications Matrix Representations Determinants Calculation Properties Relation to Invertibility Theorems Eigenvalues and Eigenvectors Definitions and Examples Characteristic Polynomial Connections to Differential Equations Diagonalization See the course calendar for details concerning exams and quizzes.