### Math 4140: Matrix Theory

**Course Description**

Basic properties of matrices, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and Jordan normal forms. Introduction to writing proofs.

**Textbook**

*Linear Algebra with Applications (7th edition)* by Steven J. Leon

**Sections Covered**

- 1.1: Systems of Linear Equations
- 1.2: Row Echelon Form
- 1.3: Matrix Algebra
- 1.4: Elementary Matrices
- 1.5: Partitioned Matrices (Optional)
- 2.1: The Determinant of a Matrix
- 2.2: Properties of Determinants
- 2.3: Cramer's Rule
- 3.1: Definition and Examples
- 3.2: Subspaces
- 3.3: Linear Independence
- 3.4: Basis and Dimension
- 3.5: Change of Basis
- 3.6: Row Space and Column Space
- 4.1: Definition and Examples
- 4.2: Matrix Representations of Linear Transformations
- 4.3: Similarity
- 5.1: The Scalar Product in Rn
- 5.2: Orthogonal Subspaces
- 5.3: Least Squares Problems (Optional)
- 5.4: Inner Product Spaces
- 5.5: Orthonormal Sets
- 5.6: The Gram-Schmidt Orthogonalization Process
- 6.1: Eigenvalues and Eigenvectors
- 6.4: Hermitian Matrices

Chapter Notes

Chapters III and IV Notes

Chapter V notes

Chapter VI notes

Suggested Problems and Assignments

Assignment Due Dates: TBA