Results 41 to 50 of about 2,762,818 (340)
The Numerical Range of 6 Χ 6 Irreducible Matrices [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2007 In this paper, we consider the problem of characterizing the numerical range of 6 by 6 irreducible matrices which have line segments on their boundary.
Ahmed Sabir
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On the elliptical range theorems for the Davis-Wielandt shell, the numerical range, and the conformal range [PDF]
arXiv, 2022 The conformal range, which is a horizontal projection of the Davis-Wielandt shell, can be considered as the hyperbolic version of the numerical range. Here we explain (the analogue of) the elliptical range theorem of $2\times2$ complex matrices for the conformal range.
arxiv
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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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
Charles A. Akemann, Joel Anderson
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On the convexity of the quaternionic essential numerical range [PDF]
arXiv, 2022 The numerical range in the quaternionic setting is, in general, a non convex subset of the quaternions. The essential numerical range is a refinement of the numerical range that only keeps the elements that have, in a certain sense, infinite multiplicity. We prove that the essential numerical range of a bounded linear operator on a quaternionic Hilbert
arxiv
Discontinuity of maximum entropy inference and quantum phase transitions
New Journal of Physics, 2015 In this paper, we discuss the connection between two genuinely quantum phenomena—the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference
Jianxin Chen +7 more
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Numerical Range of Moore–Penrose Inverse Matrices
Mathematics, 2020 Let A be an n-by-n matrix. The numerical range of A is defined as W ( A ) = { x * A x : x ∈ C n , x * x = 1 } . The Moore–Penrose inverse A + of A is the unique matrix satisfying A A + A = A , A + A A + = A ...
Mao-Ting Chien
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Joint Numerical Range of Matrix Polynomials [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2009 Some algebraic properties of the sharp points of the joint numerical range of a matrix polynomials are the main subject of this paper. We also consider isolated points of the joint numerical range of matrix polynomials.
Ahmed Sabir
doaj +1 more source
Numerical ranges of the product of operators [PDF]
Operators and Matrices, 2017 We study containment regions of the numerical range of the product of operators $A$ and $B$ such that $W(A)$ and $W(B)$ are line segments. It is shown that the containment region is equal to the convex hull of elliptical disks determined by the spectrum of $AB$, and conditions on $A$ and $B$ for the set equality holding are obtained.
Kuo-Zhong Wang +4 more
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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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