Math 320, Spring 2005

1. A factorization of symmetric matrices: "Every (real or complex) symmetric matrix S may be factored as S=M^T M where M is a square matrix and M^T is the transpose of M." (proof, examples/numerical implementation)

2. A property of symmetric matrices: "Every square matrix is similar to a symmetric matrix." (proof, examples/numerical implementation)

3. Positive matrices: Characterization, basic properties, applications

KERİM HAS

4. Vandermonde matrices: Characterization, basic properties, applications

5. Matrix norms: Possible norms, their relation, applications, etc.

6. Quadratic forms and Sylvester's law of inertial for a finite-dimensional complex vector space: Characterization, basic properties, examples

7. Perturbative solution of the eigenvalue problem for a self-adjoint operator: Characterization, basic properties, examples

8. Variational solution of the eigenvalue problem for a self-adjoint operator: Characterization, basic properties, examples

ÖĞÜNÇ TEVFİK HATİPOĞLU

9. Numerical Solutions of the Eigenvalue problem for a Large Hermitian Matrix: General discussion, specifically efficient methods, examples/numerical implementation

ÖZGÜN YEŞİLYURT

10. Antilinear operators: Characterization, basic properties, applications