REU at Kent State University

Applications and Ramifications of Linear Algebra

Mailing address

REU program
Dept. of Math Sciences
Kent State University
Math & CS Building
Summit Street, Kent OH 44242


Jenya Soprunova
reu [at]
TEL: (330)672-9086
FAX: (330) 672-2209

REU 09

Participants: Toan Duc Dinh, Michael Donzella, Thomas Dinitz, Matthew Hartman, Lizbee Collins-Wildman, Matthew Hoffman, Benjamin Mackey, Catherine Pizzano
Advisors: Mikhail Chebotar, Jenya Soprunova, Andrew Tonge, Laura Smithies
Papers produced:

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

REU 09