Professional Interests
structured eigenvectors
interlacing
matrix completions
totally nonnegative matrices
zero forcing number
Twin Cities Math Teachers' Circle
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, structured eigenvectors, totally nonnegative matrices,and zero forcing number.
I am one of the co-organizers of Minnesota's first Math Teachers' Circle called the Twin Cities Math Teachers' Circle (TCMTC). Myself, Melissa Loe and Cheri Shakiban from University of St. Thomas together with Minneapolis middle school teachers Patty DeJarLais and Chris Wernimont started the circle in August 2010. There are currently 18 members of the TCMTC and we meet each month to work on interesting math problems and improve the problem solving skills of the middle school math teachers who are members. We hope to energize these teachers so they bring their enthusiasm and improved problem solving skills back to their classrooms.
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.