Professional Interests
structured eigenvectors
interlacing
matrix completion

I received my PhD in Matrix Theory from the College of William and Mary. Prior to that I worked in industry for a number of years including three years for an options and futures trading firm in the Chicago Board of Trade. My research interests include matrix completion problems, eigenvalue interlacing and structured eigenvectors. I am currently working on extensions of matrix completion

Education:

• Ph.D., Applied Science Program ( Mathematics Track) College of William and Mary, 1996.
• M.S., Mathematical Sciences, Clemson University, 1987 .
• B.A., Mathematics and Chemistry, St. Olaf College, 1985.
  

Publications:

• Principal Submatrices, Geometric Multiplicities, and Structured Eigenvectors, C.R. Johnson, and B.K. Kroschel, SIAM J. Matrix Anal. Appl, 16-3 (1995) 1004-1012.
• The Euclidean Distance Completion Problem: Cycle Completability, C.R. Johnson, C.A. Jones, and B.K. Kroschel, Linear and Multilinear Algebra, 39 (1995) 195-207.
• An Interior-Point Method for Approximate Positive Semidefinite Completions, C.R. Johnson, B.K. Kroschel, and H. Wolkowicz, Computational Optimization and Applications, accepted.
• Extended Interlacing Intervals, C.R. Johnson, R.O. Hill, and B.K. Kroschel, Linear Algebra and its Applications, accepted.
• The "Clock Hands" Computer Graphics Program, C.R. Johnson and B.K. Kroschel, College Journal of Mathematics, to appear.
• The P-matrix Completion Problem, C.R. Johnson and B.K. Kroschel, Electronic Journal of Linear Algebra, vol 1.
• The Totally Nonnegative Completion Problem, C.R. Johnson, B.K. Kroschel, and M. Lundquist, Fields Institute Communications, to appear.