Shells of matrices in indefinite inner product spaces
نویسندگان
چکیده
منابع مشابه
Ela 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 ...
متن کاملShells 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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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...
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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...
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We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay) = B(x, y) on a vector space over F in the following cases: • F is an algebraically closed field of characteristic different from 2 or a real closed field, and B is symmetric or skew-symmetric; • F is an algebraically closed field of characteristic 0 or the skew field of qu...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2002
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1074