Eigenvalue computation for unitary rank structured matrices
Journal of Computational and Applied Mathematics
Unitary rank structured matrices
Journal of Computational and Applied Mathematics
On the closed representation for the inverses of Hessenberg matrices
Journal of Computational and Applied Mathematics
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In this paper we investigate some matrix structures on $\cee^{n\times n}$ 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 $\Lam_k\in\mathbb{C}^{m \times m}$, for suitable m, and with Fiedler and Markham's theorem corresponding to the limiting cases $\Lam_k\to 0$ and $\Lam_k\to\infty I$.