Results 21 to 30 of about 419,543 (296)
Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
Demonstratio Mathematica, 2021 Let ℋ{\mathcal{ {\mathcal H} }} be a complex Hilbert space and ℬ(ℋ){\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) denotes the algebra of all bounded linear operators acting on ℋ{\mathcal{ {\mathcal H} }}.
Mesbah Nadia +2 more
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Circularity of the numerical range
Linear Algebra and its Applications, 1994 AbstractAn equivalent condition on a 3-square complex or a 4-square real upper triangular matrix is found for its numerical range to be a circular disk centered at the origin. Sufficient conditions for the circularity of the numerical range of certain sparse matrices are also given in terms of graphs.
Bit-Shun Tam, Mao-Ting Chien
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Inverse Numerical Range and Determinantal Quartic Curves
Mathematics, 2020 A hyperbolic ternary form, according to the Helton–Vinnikov theorem, admits a determinantal representation of a linear symmetric matrix pencil. A kernel vector function of the linear symmetric matrix pencil is a solution to the inverse numerical range ...
Mao-Ting Chien, Hiroshi Nakazato
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Polynomials and Numerical Ranges [PDF]
Proceedings of the American Mathematical Society, 1988 Let A A be an n × n n \times n complex matrix. For 1 ≤ k ≤ n 1 \leq k \leq n we study the inclusion relation for the following polynomial sets related to the matrix A A . (a) The classical numerical range of the k
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On 3-by-3 row stochastic matrices
Special Matrices, 2023 The known constructive tests for the shapes of the numerical ranges in the 3-by-3 case are further specified when the matrices in question are row stochastic. Auxiliary results on the unitary (ir)reducibility of such matrices are also obtained.
Pham Nhi, Spitkovsky Ilya M.
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Journal of Mathematical Analysis and Applications, 2003 AbstractExistence of the fractional powers is established in Banach algebra setting, in terms of the numerical ranges of elements involved. The behavior of the spectra and (for Hermitian ∗-algebras satisfying some additional hypotheses) the ∗-numerical range under taking these powers also is investigated.
Ilya M. Spitkovsky +2 more
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Sesquilinear version of numerical range and numerical radius
Acta Universitatis Sapientiae: Mathematica, 2017 In this paper by using the notion of sesquilinear form we introduce a new class of numerical range and numerical radius in normed space 𝒱, also its various characterizations are given. We apply our results to get some inequalities.
Moradi Hamid Reza +3 more
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Some results on Drazin-Dagger matrices, reciprocal matrices, and conjugate EP matrices [PDF]
Journal of Mahani Mathematical ResearchIn this paper, a class of matrices, namely, Drazin-dagger matrices, in which the Drazin inverse andthe Moore-Penrose inverse commute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated.
Mahdiyeh Mortezaei +1 more
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Generalization of numerical range of polynomial operator matrices
Tikrit Journal of Pure Science, 2023 Suppose that is a polynomial matrix operator where for , are complex matrix and let be a complex variable. For an Hermitian matrix , we define the -numerical range of polynomial matrix of as , where .
Darawan Zrar Mohammed, Ahmed Muhammad
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Normality and the numerical range
Linear Algebra and its Applications, 1976 AbstractIt is well known that if A is an n by n normal matrix, then the numerical range of A is the convex hull of its spectrum. The converse is valid for n ⩽ 4 but not for larger n. In this spirit a characterization of normal matrices is given only in terms of the numerical range.
Charles R. Johnson, Charles R. Johnson
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