### 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