Title: Structures preserved by matrix inversion
Authors: Delvaux, Steven ×
Van Barel, Marc #
Issue Date: 2006
Publisher: Society for Industrial and Applied Mathematics
Series Title: SIAM Journal on Matrix Analysis and Applications vol:28 issue:1 pages:213-228
Abstract: In this paper we investigate some matrix structures on C-nXn that have a good behavior 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, the inverse matrix also must have a low rank submatrix, which we can explicitly determine. This allows us to generalize a theorem due to Fiedler and Markham. The generalization consists in the fact that our rank structures may have a certain correction term, which we call the shift matrix Lambda(k) is an element of C-mXm, for suitable m, and with Fiedler and Markham's theorem corresponding to the limiting cases Lambda(k) -> 0 and Lambda(k) -> infinity I.
ISSN: 0895-4798
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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