Results 21 to 30 of about 604,967 (307)
Investigating the numerical range and q-numerical range of non square matrices [PDF]
Opuscula Mathematica, 2011 A presentation of numerical ranges for rectangular matrices is undertaken in this paper, introducing two different definitions and elaborating basic properties. Further, we extend to the \(q\)-numerical range.
Aikaterini Aretaki, John Maroulas
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Some Results on Polynomial Numerical Hulls of Perturbed Matrices [PDF]
Sahand Communications in Mathematical Analysis, 2019 In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.
Madjid Khakshour, Gholamreza Aghamollaei
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On partial isometries with circular numerical range
Concrete Operators, 2021 In their LAMA 2016 paper Gau, Wang and Wu conjectured that a partial isometry A acting on ℂn cannot have a circular numerical range with a non-zero center, and proved this conjecture for n ≤ 4. We prove it for operators with rank A = n − 1 and any n.
Wegert Elias, Spitkovsky Ilya
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Quaternionic numerical range of complex matrices [PDF]
, 2023 This paper explores further the computation of the quaternionic numerical range of a complex matrix. We prove a modified version of a conjecture by So and Thompson.
Diogo, C., Mendes, S., Carvalho, L.
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On joint numerical ranges [PDF]
Pacific Journal of Mathematics, 1978 The joint numerical status of commuting bounded operators Ai and A2 on a Hubert space is defined as {{φiA^y φ(A2)) such that φ is a state on the C*-algebra generated by Ax and A2}. It is shown that if At and A2 are commuting normal operators then their joint numerical status equals the closure of their joint numerical range.
Buoni, John J., Wadhwa, Bhushan L.
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From the Kirsch-Kress potential method via the range test to the singular sources method
, 2022 We review three reconstruction methods for inverse obstacle scattering problems. We will analyse the relation between the Kirsch-Kress potential method 1986, the range test of Kusiak, Potthast and Sylvester (2003) and the singular sources method of ...
Schulz, J. +3 more
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Joint numerical ranges: recent advances and applications minicourse by V. Müller and Yu. Tomilov
Concrete Operators, 2020 We present a survey of some recent results concerning joint numerical ranges of n-tuples of Hilbert space operators, accompanied with several new observations and remarks.
Müller V., Tomilov Yu.
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THE SPECTRAL SCALE AND THE NUMERICAL RANGE [PDF]
International Journal of Mathematics, 2003 Suppose that c is an operator on a Hilbert Space H such that the von Neumann algebra N generated by c is finite. Let τ be a faithful normal tracial state on N and set b1= (c + c*)/2 and b2= (c - c*)/2i. Also write B for the spectral scale of {b1, b2} relative to τ. In previous work by the present authors, some joint with Nik Weaver, B has been shown to
Akemann, Charles A., Anderson, Joel
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The essential numerical range for unbounded linear operators [PDF]
, 2020 We introduce the concept of essential numerical range W_e(T) for unbounded Hilbert space operators T and study its fundamental properties including possible equivalent characterizations and perturbation results.
Bögli, Sabine +2 more
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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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