Algebra, Combinatorics, and Number Theory Seminar
Ross Hall 247
3:10pm, Tuesday, 29 April 2014
Title: Using Jacobian method to find (more) skew-symmetric matrices with prescribed eigenvalues.
Abstract: Previously, it was seen that one can find a skew-symmetric matrix whose graph is a certain tree (e.g. a path) with prescribed distinct eigenvalues. For example, there is a tridiagonal matrix whose eigenvalues are -2i, -i, i, 2i. Are there any more matrices (not a permutation of indices) with this spectrum? Is there any skew-symmetric matrix whose eigenvalues are -2i, -i, i, 2i, where all the off-diagonal entries are nonzero?
The Jacobian method is developed to find more solutions to some problems, when there is a generic solution in hand. In this talk, we hire the power of the Jacobian method to find skew-symmetric matrices where the eigenvalues are fixed distinct (purely imaginary) numbers, and a graph (zero-nonzero pattern) is given.
This is joint work with Sudipta Mallik.