Results 21 to 30 of about 2,436,536 (336)

Reduction of the c-numerical range to the classical numerical range

Linear Algebra and its Applications, 2011
For an \(n\)-by-\(n\) complex matrix \(A\) and a real \(n\)-tuple \(c=(c_1,\dots, c_n)\), the \(c\)-numerical range \(W_c(A)\) of \(A\) is, by definition, the subset \[ \Biggl\{\sum^n_{j=1} c_j x^*_j Ax_j: x_1,\dots, x_n\text{ form an orthonormal basis of }\mathbb{C}^n\Biggr\} \] of the complex plane.
Chien, Mao-Ting, Nakazato, Hiroshi
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On generalized numerical ranges [PDF]

Pacific Journal of Mathematics, 1976
which ||(T- viyι\\ = l/d(υ, W(T)), v£ CLW(T), where CLW(T) is the closure of the numerical range W(T) of Γ, has been generalized by using the concept of generalized numerical ranges due to C. S. Lin. Also it has been shown that the notions of generalized Minkowski distance functionals and generalized numerical ranges arise in a natural way for elements
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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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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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High numerical aperture holographic microscopy reconstruction with extended z range [PDF]

, 2015
An holographic microscopy reconstruction method compatible with high numerical aperture microscope objective (MO) up to NA=1.4 is proposed. After off axis and reference field curvature corrections, and after selection of the +1 grating order holographic ...
Donnarumma, Dario, Gross, Michel, Tessier, Gilles, Verrier, Nicolas   +3 more
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On numerical ranges and roots

Journal of Mathematical Analysis and Applications, 2003
Let \({\mathfrak a}\) be a complex Banach algebra with unit \(e\). The algebraic numerical range \(V(a)\) of an element \(a\) in \({\mathfrak a}\) is the set \(\{f(a): f\) is a bounded linear functional on \({\mathfrak a}\) such that \(f(e)= \| f\|=1\}\).
Li, Chi-Kwong, Rodman, Leiba, Spitkovsky, Ilya M.   +2 more
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Spatial numerical ranges of elements of subalgebras of C0(X)

International Journal of Mathematics and Mathematical Sciences, 2000
When A is a subalgebra of the commutative Banach algebra C0(X) of all continuous complex-valued functions on a locally compact Hausdorff space X, the spatial numerical range of element of A can be described in terms of positive measures.
Sin-Ei Takahasi
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Enclosure of the Numerical Range of a Class of Non-Selfadjoint Rational Operator Functions [PDF]

, 2017
In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the finite ...
Engström, Christian, Torshage, Axel
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Some results on Drazin-Dagger matrices, reciprocal matrices, and conjugate EP matrices [PDF]

Journal of Mahani Mathematical Research
In 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, Gholamreza Aghamollaei   +1 more
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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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