2 research outputs found
On the Linear Algebraic Monoids Associated to Congruence of Matrices
This paper discusses the generalized congruence equation , for over any field , through the action of monoid . We have
completely characterized for what matrices , the monoid is a Lie
group. We have given the structure of the Lie group and ,
and their Lie algebras when is nilpotent matrix of nilpotency
. In this case, we have also proved that the invariants of for any
, and for even, are finitely generated
On perturbations of matrix pencils with real spectra. II
A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A and à be two nxn Hermitian matrices, and let λ1,...,λn and λ1,...,λn be their eigenvalues arranged in ascending order. Then diag |||(λ1-λ1,...,λn-λn) ≤|||A-Ã||| for any unitarily invariant norm ||| .|||. In this paper, we generalize this to the perturbation theory for diagonalizable matrix pencils with real spectra. The much studied case of definite pencils is included in this