REU at Kent State University

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REU 09

Toan Duc Dinh, Michael Donzella, On maps preserving zeroes of Lie polynomials of small degrees, Linear Algebra and its Applications, 432, Issues 2-3, (2010), p. 493-498.
Abstract: We describe maps preserving zeros of multilinear Lie polynomials of degrees 3 and 4 on prime algebras and matrices over unital algebras. In particular, our theorems generalize several results related to commutativity preserving maps.

Thomas Dinitz, Matthew Hartman, and Jenya Soprunova, Tropical Determinant of Integer Doubly-Stochastic Matrices, Linear Algebra and its Applications 436, Issue 5 (2012), 1212-1227.
Abstract: Let D(m,n) be the set of all the integer points in the m-dilate of the Birkhoff polytope of doubly-stochastic n by n matrices. In this paper we find the sharp upper bound on the tropical determinant over the set D(m,n). We define a version of the tropical determinant where the maximum over all the transversals in a matrix is replaced with the minimum and then find the sharp lower bound on thus defined tropical determinant over D(m,n).

Lizbee Collins-Wildman and Matthew Hoffman, Matrices with small operator norm, submitted.

Bren Cavallo, Lynne DeYoung, and Benjamin Mackey, Catherine Pizzano, and Laura Smithies (results of REU 09 and REU 10), Decompositions of Tridiagonal Nearly Normal Matrices