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.

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