Professor of Mathematics Leo Livshits and Joshua Hews ’17 have published an original research article in the Electronic Journal of Linear Algebra. Titled “Groups of Matrices That Act Monopotently” the paper deals with the properties of the eigenvalues of a complex matrix, which are complex numbers associated with the matrix that capture some essential information about its behavior. Eigenvalues of a composition of two matrices may be quite different from those of the original matrices. When a matrix with a single eigenvalue is composed with a group of other matrices, the resulting matrices may not all have just a single eigenvalue. The authors prove that this will indeed be the case for a large class of matrix groups. The paper reflects a collaboration between Livshits and Hews that was supported by the Colby Summer Student Research Fund. Hews is currently in a graduate program in mathematics at the University of Waterloo in Canada.
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