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