Linear Algebra - Foundations to Frontiers

Description

In this course, you will learn:

• Relationships between linear transformations, matrices, and linear equation systems.
• Partitioned matrices and special matrices' properties
• Algorithms for solving systems of equations and computing matrices.
• Linear independence characterizations, vector spaces, and subspaces
• eigenvalues and eigenvectors, orthogonality, linear least-squares

Syllabus:

1. Vectors in Linear Algebra
2. Linear Transformations and Matrices
3. Matrix-Vector Operations
4. From Matrix-Vector Multiplication to Matrix-Matrix Multiplication
5. Matrix-Matrix Multiplication
6. Gaussian Elimination
7. More Gaussian Elimination and Matrix Inversion
8. More on Matrix Inversion
9. Vector Spaces
10. Vector Spaces, Orthogonality, and Linear Least Squares
11. Orthogonal Projection and Low-Rank Approximation
12. Eigenvalues and Eigenvectors