Results 31 to 40 of about 2,226,866 (302)
A characterization of the definiteness of a Hermitian matrix [PDF]
Glasgow Mathematical Journal, 1974 We denote by F the field R of real numbers, the field C of complex numbers or the skew-field H of real quaternions, and by Fn an n-dimensional left vector space over F. If A is a matrix with elements in F, we denote by A* its conjugate transpose. In all three cases of F, an n × n matrix A is said to be hermitian (unitary resp.) if A = A* (AA*= identity
Tai-Kwok Yuen, Yik-Hoi Au-Yeung
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The scattering matrix with respect to an Hermitian matrix of a graph
Discrete Mathematics, 2022 21 pages.
Takashi Komatsu, Norio Konno, Iwao Sato
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Entanglement, non-hermiticity, and duality
SciPost Physics, 2021 Usually duality process keeps energy spectrum invariant. In this paper, we provide a duality, which keeps entanglement spectrum invariant, in order to diagnose quantum entanglement of non-Hermitian non-interacting fermionic systems.
Li-Mei Chen, Shuai A. Chen, Peng Ye
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How much can the eigenvalues of a random Hermitian matrix fluctuate? [PDF]
Duke mathematical journal, 2019 The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues.
T. Claeys +3 more
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Implementing smooth functions of a Hermitian matrix on a quantum computer [PDF]
Journal of Physics Communications, 2018 We consider methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has advantages of simplicity and resource consumption in some cases.
Sathyawageeswar Subramanian +2 more
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On relative residual bounds for the eigenvalues of a Hermitian matrix
Linear Algebra and its Applications, 1996 Let $H$ be a Hermitian matrix, $ X$ an orthonormal matrix, and $M=X^*H X$. Then the eigenvalues of $M$ approximate some eigenvalues of $H$ with an absolute error bounded by $\| HX-XM\|_2$. The main interest in this work is the relative distance between the eigenvalues of $M$ and some part of the spectrum of $H$. It is shown that distance depends on the
Zlatko Drmač
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Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach [PDF]
Journal of High Energy Physics, 2018 A bstractUsing large N arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large N limit.
M. Nowak, W. Tarnowski
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Density-matrix formalism for PT -symmetric non-Hermitian Hamiltonians with the Lindblad equation [PDF]
Physical Review A, 2020 In the presence of Lindblad decoherence, i.e. dissipative effects in an open quantum system due to interaction with an environment, we examine the transition probabilities for "mass" and "flavor" eigenstates in the two-level quantum system described by ...
T. Ohlsson, Shun Zhou
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European Physical Journal C: Particles and Fields, 2022 We construct the ( $$\beta $$ β -deformed) partition function hierarchies with W-representations. Based on the W-representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur functions and ...
Rui Wang +3 more
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Asymmetric Hermitian matrix models and fuzzy field theory [PDF]
Physical Review D, 2017 We analyze two types of hermitian matrix models with asymmetric solutions. One type breaks the symmetry explicitly with an asymmetric quartic potential. We give the phase diagram of this model with two different phase transitions between the one cut and ...
J. Tekel
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