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TW 414
Steven Delvaux, Marc Van Barel
Structures preserved by matrix inversion
Abstract
In this paper we investigate some matrix structures on Cn x n that have a good behaviour under matrix inversion. The first type of structure is closely related to low displacement rank matrices. Next, we show that for a matrix having a low rank submatrix, also the inverse matrix must have a low rank submatrix, which we can explicitly determine. This allows us to generalize a theorem due to Fiedler. The generalization consists in the fact that our rank structures may have their own shift matrix Λk ∈ Cm x m, for suitable m, with Fiedler's theorem corresponding to the limiting cases Λk → 0 and Λk → ∞
report.pdf (265K) / mailto: S. Delvaux