On a pathology in indefinite metric inner product space
نویسندگان
چکیده
منابع مشابه
On 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 کاملOn Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space
In this paper, numerical ranges associated to operators on an indefinite inner product space are investigated. Boundary generating curves, corners, shapes and computer generations of these sets are studied. In particular, the MurnaghanKippenhahn theorem for the classical numerical range is generalized.
متن کاملEla Numerical Ranges of an Operator on an Indefinite Inner Product Space
For n n complex matrices A and an n n Hermitian matrix S, we consider the S-numerical range of A and the positive S-numerical range of A de ned by WS(A) = hAv; viS hv; viS : v 2 I Cn; hv; viS 6= 0
متن کاملCanonical matrices of isometric operators on indefinite inner product spaces
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...
متن کاملNumerical ranges of an operator on an indefinite inner product space
For n n complex matrices A and an n n Hermitian matrix S, we consider the S-numerical range of A and the positive S-numerical range of A de ned by WS(A) = hAv; viS hv; viS : v 2 I Cn; hv; viS 6= 0
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1982
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02029137