Hugo J. Woerdeman, Department of Mathematics

Possible Undergraduate Research Projects

I have a wide range of interests in mathematics and I enjoy doing research with undergraduate students on various topics. This can be funded through my NSF grant which has a Research Experiences for Undergraduates (REU) component. In the past, I have conducted undergraduate research projects on matrix theory, operator theory and harmonic analysis. It helps a lot if you have had an undergraduate Linear Algebra course, as my research uses Linear Algebra extensively. You are welcome to make an appointment with me to discuss possible projects.

Here is a list of specific problems.

• Describe submatrices of normal matrices.
• Find efficient algorithms for inverses of multilevel structured matrices.
• Find effective ways to perform factorizations of trigonometric polynomials.
• Describe certain convex sets as intersections of halfspaces, and use this description to devise an optimization algorithm.
• Solve the minimal rank uniqueness problem for banded matrices.
• Find the minimal negative inertia completion for banded Toeplitz matrices.
• etc.

The following papers are peer reviewed articles that I have written with undergraduate students:

• Minimal normal and commuting completions, with D. P. Kimsey, In: Special issue "Matrix Analysis and Applications" of the International J. of Information & Systems Sciences 4 (2008), 50--59. (Click here for full text)
• Spectral factorizations and sums of squares representations via semidefinite programming, with J. W. McLean, SIAM J. Matrix Anal. Appl. 23 (2001/02), 646-655. (Click here for full text)
• Uniticity of minimal rank completions for tri-diagonal partial block matrices, with A. A. Bostian, Linear Algebra Appl. 325 (2001), 23--55. (Click here for full text)
• The Maximum Row Sum Nonsingularity Radius, with B. I. Wainberg, Linear Algebra Appl. 247 (1996), 251-264. (Click here for full text)
• Sparsity Patterns with High Rank Extremal Semipositive Definite Matrices, with J.W. Helton and D.Lam, SIAM J. Matrix Anal. Appl. 15 (1994), 299-312. (Click here for full text)