Classes of plus matrices in finite dimensional indefinite scalar product spaces
نویسندگان
چکیده
منابع مشابه
On Indecomposable Normal Matrices in Spaces with Indefinite Scalar Product
Finite dimensional linear spaces (both complex and real) with indefinite scalar product [·, ·] are considered. Upper and lower bounds are given for the size of an indecomposable matrix that is normal with respect to this scalar product in terms of specific functions of v = min{v − , v+}, where v− (v+) is the number of negative (positive) squares of the form [x, x]. All the bounds except for one...
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Polar decompositions X = U A of real and complex matrices X with respect to the scalar product generated by a given indefinite nonsingular matrix Hare studied in the following special cases: (1) X is an H-contraction, (2) X is an H-plus matrix, (3) H has only one positive eigenvalue, and (4) U belongs to the connected component of the identity in the group of H-unitary matrices. Applications to...
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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: Integral Equations and Operator Theory
سال: 1998
ISSN: 0378-620X,1420-8989
DOI: 10.1007/bf01257876