2-dimensional subspaces of M_n(F) containing many elements of different ranks
Speaker: Dr. Kevin Jennings (NUIG)
Time: 4:00pm
Date: Monday February 10th 2014
Location: CASL Seminar Room, Block 8, Belfield Office Park
Abstract:
Let U be a 2-dimensional subspace of M_n(F), so U = {sA+tB} for matrices A and B in M_n(F) and scalars s and t in F. F will often be a finite field F_q. We investigate how many distinct ranks can occur amongst elements of U. Some elementary combinatoric bounds are easily obtained and some natural cases can be proved optimal using elementary linear algebra. We answer the question "For given n, what is the maximal number t of distinct ranks which can occur in U?" using a result of Kronecker. Further questions abound.
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