Results 31 to 40 of about 419,543 (296)
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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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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Numerical shadows: Measures and densities on the numerical range [PDF]
Linear Algebra and its Applications, 2011 For any operator $M$ acting on an $N$-dimensional Hilbert space $H_N$ we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of $M$. The shadow of $M$ at point $z$ is defined as the probability that the inner product $(Mu,u)$ is equal to $z$, where $u$ stands for a random complex vector ...
John Holbrook +4 more
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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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The Boundary of the Numerical Range [PDF]
Proceedings of the American Mathematical Society, 1975 This work includes two results which indicate a set theoretic relationship between the boundary of the numerical range and the essential numerical range. Several applications are derived.
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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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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
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Spectral sets for numerical range [PDF]
Operators and Matrices, 2017 We define and study a numerical-range analogue of the notion of spectral set. Among the results obtained are a positivity criterion and a dilation theorem, analogous to those already known for spectral sets. An important difference from the classical definition is the role played in the new definition by the base point.
Javad Mashreghi +2 more
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Canopy height model and NAIP imagery pairs across CONUS
Scientific DataCanopy height models (CHM) provide detailed environmental vertical structure information and are an important indicator and input for ecological and geospatial applications.
Brady W. Allred +2 more
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