When do two square matrices "commute"?
April 7, 2014
Bailey Hall 207
Refreshments will be served in Bailey Hall 204 4:45pm
One of the first things that we learn about multiplication of matrices is that it is not "commutative", that is if A and B are two square matrices of the same size then in general AB is not the same as BA. However, we can easily think of pairs of matrices that do "commute", e.g. if one of the matrices is the identity matrix or the zero matrix, or if A and B are both the same, then we have AB=BA. So it is natural to ask: which pairs of matrices do in fact commute? The goal of this talk is to present a refined version of this natural question, using one of the most important classical theorems in linear algebra, the Jordan Decomposition Theorem. We are going to introduce a game which will help us understand the main idea of Jordan decomposition theorem, as well as the question of commuting pairs of matrices.
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