Rank related dimension bounds for subspaces of matrices and bilinear forms.
Title: Rank related dimension bounds for subspaces of matrices and bilinear forms.
Speaker: Rod Gow (UCD)
Date: Monday, 15th February 2016
Time: 4pm
Location: Agriculture. 1.01 (Seminar Room).
Abstract:
We proved last year that a constant rank r subspace of n x n matrices over a finite field has dimension at most n, provided the field contains at least r+1 elements.
We show how this constant rank dimension bound can be used to obtain further dimension bounds when there are just two ranks involved in the subspace. We examine symmetric and skew-symmetric matrices from this rank point of view and obtain some interesting decompositions in terms of spreads in certain special cases.
We also describe dimension bounds that hold for odd rank subspaces of symmetric matrices over an arbitrary field.
Series: Algebra
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