Results 11 to 20 of about 513,360 (262)
On the Numerical Range and Numerical Radius of the Volterra Operator
Известия Иркутского государственного университета: Серия "Математика", 2018 In this paper, we investigated the numerical range and the numerical radius of the classical Volterra operator on the complex space $L^2[0,1]$. In particular, we determined the numerical range, the numerical radius of real and imaginary part of the ...
L. Khadkhuu, D. Tsedenbayar
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Numerical range of a continuant matrix
Applied Mathematics Letters, 2001 For a continuant matrix \(A\in M_n({\mathbb C})\) of a special form \(A=\left(\begin{smallmatrix} 0 & I_{n-1} \\ 0 & 0\end{smallmatrix}\right) +\text{diag} (a,b,a,b,\dotsc)+\left(\begin{smallmatrix} 0 & 0\\ -I_{n-1} & 0\end{smallmatrix}\right)\) its numerical range is explicitly described as an elliptic disc.
Mao-Ting Chien
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On the boundary of the numerical range of a matrix
Applied Mathematics Letters, 2010 Every diagonal element of a~matrix~\(A\) is known to lie in the numerical range \(W(A)\) of~\(A\). A~characterization of real \(2\times 2\) matrices~\(A\) for which a~diagonal entry is a~boundary point of its numerical range is obtained, and is as follows: the diagonal entry~\(a_{11}\) is a~boundary point of the numerical range of~\(A\) if and only if \
Mao-Ting Chien
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Essential numerical range and $C$-numerical range for unbounded operators [PDF]
Studia Mathematica, 2022 Consider an unbounded operator \(T\) on a Hilbert space \(\mathcal{H}\). The authors introduce a new type of essential numerical range for \(T\), called \(W_{e5}(T)\) (essential numerical range of type 5). They show, for instance, that \(W_{e5}(T)\) is closed, convex, and contains the essential spectrum \(\sigma_e(T)\).
Hefti, Nicolas Benjamin +1 more
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Index rank-$k$ numerical range of matrices [PDF]
Journal of Mahani Mathematical Research, 2023 We introduce the $\alpha-$higher rank form of the matrix numerical range, which is a special case of the matrix polynomial version of higher rank numerical range.
Sharifeh Rezagholi, Rouholah Yasini
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Further extensions of Hartfiel’s determinant inequality to multiple matrices
Special Matrices, 2021 Following the recent work of Zheng et al., in this paper, we first present a new extension Hartfiel’s determinant inequality to multiple positive definite matrices, and then we extend the result to a larger class of matrices, namely, matrices whose ...
Luo Wenhui
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The Numerical Range of C*ψ Cφ and Cφ C*ψ
Concrete Operators, 2021 In this paper we investigate the numerical range of C*bφm Caφn and Caφn C*bφm on the Hardy space where φ is an inner function fixing the origin and a and b are points in the open unit disc.
Clifford John +2 more
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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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The numerical range and the essential numerical range [PDF]
Proceedings of the American Mathematical Society, 1977 A simple proof is given of Lancaster’s theorem that the convex hull of the numerical and essential numerical ranges of a Hilbert space operator is the closure of the numerical range.
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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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