Classes of normal matrices in indefinite inner products
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 کاملOn classification of normal matrices in indefinite inner product spaces
Canonical forms are developed for several sets of matrices that are normal with respect to an indefinite inner product induced by a nonsingular Hermitian, symmetric, or skewsymmetric matrix. The most general result covers the case of polynomially normal matrices, i.e., matrices whose adjoint with respect to the indefinite inner product is a polynomial of the original matrix. From this result, c...
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 Essential Decomposition of Polynomially Normal Matrices in Real Indefinite Inner Product Spaces∗
Polynomially normal matrices in real indefinite inner product spaces are studied, i.e., matrices whose adjoint with respect to the indefinite inner product is a polynomial in the matrix. The set of these matrices is a subset of indefinite inner product normal matrices that contains all selfadjoint, skew-adjoint, and unitary matrices, but that is small enough such that all elements can be comple...
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...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2001
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00299-3