Professor: Leonardo Colò
Course code: MATH 225
Section: 081
Workload: Jan-Apr 2025 (12 weeks)
Delivery method: Online

1. Abstract Vector Spaces (2 weeks):
   - Vector space axioms.
   - Subspaces.
   - Basis and dimension.
   - Coordinates.
2. Linear Mappings (3 weeks):
   • - Definition and examples.
     - Range and nullspace.
     - Vector space isomorphisms.
     - Matrix of a linear mapping
     - Diagonalization.
3. Inner Product Spaces (4 weeks):
   • - Introduction to inner product spaces.
     - Inner products on \(\mathbb{R}^n\).
     - Orthogonality.
     - Method of least squares.
     - General inner product spaces.
     - Orthogonality.
     - Orthogonal complement.
4. Orthogonal diagonalization and applications (3 weeks):
   • - Diagonalization of symmetric matrices.
     - Quadratic forms.
     - Singular value decomposition.
     - Optimization (linear programming).
     - Infinite dimensional inner product spaces.