Results 11 to 20 of about 242,274 (310)
Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State [PDF]
Journal of Statistical Physics, 2008 A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state.
Arul Lakshminarayan +2 more
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Bounds and optimization of the minimum eigenvalue for a vibrating system
Electronic Journal of Qualitative Theory of Differential Equations, 2013 We consider the problem of the oscillation of a string fixed at one end with a mass connected to a spring at the other end. The problem of minimizing the first eigenvalue of the system subject to a fixed total mass constraint is investigated.
Don Hinton, Maeve McCarthy
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Linear Algebra and its Applications, 2023 referee improvements ...
Aida Abiad +7 more
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Two new lower bounds for the minimum eigenvalue of M-tensors [PDF]
Journal of Inequalities and Applications, 2016 Two new lower bounds for the minimum eigenvalue of an irreducible M-tensor are given. It is proved that the new lower bounds improve the corresponding bounds obtained by He and Huang (J. Inequal. Appl. 2014:114, 2014).
Jianxing Zhao, Caili Sang
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On completely regular codes with minimum eigenvalue in geometric graphs
Discrete Mathematics, 2022 We prove that any completely regular code with minimum eigenvalue in any geometric graph G corresponds to a completely regular code in the clique graph of G. Studying the interrelation of these codes, a complete characterization of the completely regular codes in the Johnson graphs J(n,w) with covering radius w-1 and strength 1 is obtained.
I. Yu. Mogilnykh, K. V. Vorob'ev
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A lower bound for the minimum eigenvalue of the Hadamard product of matrices
Linear Algebra and its Applications, 2003 AbstractSuppose both A and B are n×n nonsingular M-matrices. An estimate from below for the smallest eigenvalue τ(A∘B−1) (in modulus) of the Hadamard product A∘B−1 of A and B−1 is derived. As a special case, we obtain the inequality τ(A∘A−1)⩾2n (n⩾2).
Chen Shen-can
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Some new inequalities for the minimum eigenvalue of M-matrices [PDF]
Journal of Inequalities and Applications, 2015 Some new inequalities for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
Feng Wang, Deshu Sun
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Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments [PDF]
Special Matrices, 2019 Abstract Considered are combinatorially symmetric matrices, whose graph is a given tree, in view of the fact recent analysis shows that the geometric multiplicity theory for the eigenvalues of such matrices closely parallels that for real symmetric (and complex Hermitian) matrices. In contrast to the real symmetric case, it is shown that
Carlos M. Saiago
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The Electronic Journal of Combinatorics, 2017 For a given graph $G$ and an associated class of real symmetric matrices whose diagonal entries are governed by the adjacencies in $G$, the collection of all possible spectra for such matrices is considered. Building on the pioneering work of Colin de Verdière in connection with the Strong Arnold Property, two extensions are devised that target a ...
Wayne Barrett +5 more
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Some applications of the new maximum-minimum theory of eigenvalues
Journal of Mathematical Analysis and Applications, 1965 Alexander Weinstein
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