Rank one perturbations of H-positive real matrices
Date
2013Author
Fourie, J.H.
Groenewald, G.J.
Janse van Rensburg, D.B.
Ran, A.C.M.
Metadata
Show full item recordAbstract
We consider a generic rank one structured perturbation on
H-positive real matrices. The case with complex rank one perturbation
is treated in general, but the main focus of this article is the
real rank one perturbation. In general, the H-positive real matrix A
which is given in Jordan canonical form loses the largest Jordan block
after a rank one perturbation for each eigenvalue. Surprisingly, for a
real H-skew symmetric matrix for which the largest Jordan block at
eigenvalue zero has even size and for a real H-nonnegative rank one
perturbation the largest Jordan block with zero eigenvalue grows one
in size. Generic Jordan structures of perturbed matrices are identified.
URI
http://hdl.handle.net/10394/14514https://doi.org/10.1016/j.laa.2013.04.010
https://www.sciencedirect.com/science/article/pii/S0024379513002723