What is a totally positive matrix?

Series: 
Research Horizons Seminar
Wednesday, October 7, 2009 - 12:00
1 hour (actually 50 minutes)
Location: 
Skiles 171
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School of Mathematics, Georgia Tech
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In linear algebra classes we learn that a symmetic matrix with real entries has real eigenvalues. But many times we deal with nonsymmetric matrices that we want them to have real eigenvalues and be stable under a small perturbation. In the 1930's totally positive matrices were discovered in mechanical problems of vibtrations, then lost for over 50 years. They were rediscovered in the 1990's as esoteric objects in quantum groups and crystal bases. In the 2000's these matrices appeared in relation to Teichmuller space and its quantization. I plan to give a high school introduction to totally positive matrices.