Generalized Finite Algorithms for Constructing Hermitian Matrices with Prescribed Diagonal and Spectrum [PDF]
, 2005 In this paper, we present new algorithms that can replace the diagonal entries of a Hermitian matrix by any set of diagonal entries that majorize the original set without altering the eigenvalues of the matrix.
Dhillon, Inderjit S. +3 more
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ESTIMATION OF THE MAXIMUM MULTIPLICITY OF AN EIGENVALUE IN TERMS OF THE VERTEX DEGREES OF THE GRAPH [PDF]
, 2002 . The maximum multiplicity among eigenvaluesof matriceswith a given graph cannot generally be expressed in terms of the degrees of the vertices (even when the graph is a tree).
Carlos +3 more
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Dimension of the intersection of a pair of orthogonal groups [PDF]
, 2009 Let $g,h\colon V\times V\rightarrow mathbb{C}$ be two non-degenerate symmetric bilinear forms on a finite-dimensional complex vector space $V$. Let $G$ (resp.\ $H$) be the Lie group of isometries of $g$ (resp.\ $h$).
Song, Seok-Zun +4 more
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Asymptotic spectral properties of totally symmetric multilevel Toeplitz matrices [PDF]
, 2002 Let n=(n1,…,nk) be a multiindex and κ(n̲)=∏j=1knj. We say that n→∞ if ni→∞, 1⩽i⩽k. If r=(r1,…,rk) and s=(s1,…,sk), let ∣r−s∣=(∣r1−s1∣,…,∣s1−sk∣). We say that a multilevel Toeplitz matrix of the form Tn̲=[t|r̲-s̲|]r̲,s̲=1̲∞̲ is totally symmetric.
Gri Espinagosa, Josep +1 more
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μ-values and spectral value sets for linear perturbation classes defined by a scalar product [PDF]
, 2011 We study the variation of the spectrum of matrices under perturbations which are self- or skew-adjoint with respect to a scalar product. Computable formulas are given for the associated μ-values.
Karow, Michael
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Critical points of the optimal quantum control landscape: a propagator approach
, 2012 Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator.
Ho, Tak-San +2 more
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Minimal hermitian matrices with fixed entries outside the diagonal [PDF]
, 2008 We survey some results concerning the problem of finding the complex hermitian matrix or matrices of least supremum norm with variable diagonal. Some qualitative general results are given and more specific descriptions are shown for the 3 x 3 case.
Andruchow, Esteban +4 more
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Classification of pairs of rotations in finite-dimensional Euclidean space
, 2008 A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous conjugation with ...
Darpö, Erik
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On universality of local edge regime for the deformed Gaussian Unitary Ensemble
, 2013 We consider the deformed Gaussian ensemble $H_n=H_n^{(0)}+M_n$ in which $H_n^{(0)}$ is a hermitian matrix (possibly random) and $M_n$ is the Gaussian unitary random matrix (GUE) independent of $H_n^{(0)}$. Assuming that the Normalized Counting Measure of
A. Lytova +23 more
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Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix
, 2008 The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a matrix $X$ with columns that form an orthonormal basis for a subspace $\X$, and a Hermitian matrix $A$, the eigenvalues of $X^HAX$ are called Ritz values of $A$ with respect to
A. V. Knyazev +4 more
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