Positive real matrices in indefinite inner product spaces and invariant maximal semidefinite subspaces
نویسندگان
چکیده
منابع مشابه
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...
متن کاملEla 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.
متن کاملEla 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...
متن کاملNormal Matrices in Degenerate Indefinite Inner Product Spaces
Complex matrices that are structured with respect to a possibly degenerate indefinite inner product are studied. Based on the theory of linear relations, the notion of an adjoint is introduced: the adjoint of a matrix is defined as a linear relation which is a matrix if and only if the inner product is nondegenerate. This notion is then used to give alternative definitions of selfadjoint and un...
متن کاملEla Shells of Matrices in Indefinite Inner Product Spaces
The notion of the shell of a Hilbert space operator, which is a useful generalization (proposed by Wielandt) of the numerical range, is extended to operators in spaces with an indefinite inner product. For the most part, finite dimensional spaces are considered. Geometric properties of shells (convexity, boundedness, being a subset of a line, etc.) are described, as well as shells of operators ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.02.002