Math 320, Spring 2015
Term-Paper Project Topics
The following is the list of some possible topics for the term-paper projects. Students taking this course should select and inform the instructor via email of 3 topics of their choice for their term-paper project (indicating their priority). This must be done before 17:00 March 23, 2015. The penalty for failing to do so is a deduction of 10 points Out of 100 from their teem-paper grade for each day passed March 23.
1. A factorization of symmetric matrices: "Every (real or complex) symmetric matrix S may be factored as S=MT M where M is a square matrix and MT 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
4. Matrix norms: Possible norms, their relation, applications, etc.
5. Quadratic forms and Sylvester's law of inertial for a finite-dimensional complex vector space: Characterization, basic properties, examples
6. Perturbative solution of the eigenvalue problem for a self-adjoint operator: Characterization, basic properties, examples
7. Variational solution of the eigenvalue problem for a self-adjoint operator: Characterization, basic properties, examples
8. Antilinear operators: Characterization, basic properties, applications