Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products

Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products

It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant subspace always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative invariant subspace is actually neutral. An e...

Ela Hyponormal Matrices and Semidefinite Invariant Subspaces in Indefinite Inner Products

It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant subspace always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative invariant subspace is actually neutral. An e...

Ela Real and Complex Invariant Subspaces for Matrices Which Are H-positive Real in an Indefinite Inner Product Space

In this paper, the equivalence of the existence of unique real and complex A-invariant semidefinite subspaces for real H-positive real matrices are shown.

Quasihyponormal and strongly hyponormal matrices in inner product spaces

Ela Invariant Neutral Subspaces for Hamiltonian Matrices

Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...