Self-inversive matrix polynomials with semisimple spectrum on the unit circle
, 2011 The spectrum of a class of self-inversive matrix polynomials is studied. It is shown that the characteristic values are semisimple and lie on the unit circle if the inner radius of an associated matrix polynomial is greater than 1 .
N. Ito, R. Küstner, H. K. Wimmer
semanticscholar +1 more source
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
core +2 more sources
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
core +1 more source
Essentially hermitian matrices and inclusion relations of C -numerical ranges
, 2009 Let M denote the set of all n× n complex matrices and Mn denote the set of n× n matrices with trace 0 . For any C ∈ Mn , there exists a maximal ν(C) 0 such that ν(C)WD(A) ⊆ ‖D‖FWC(A) whenever D ∈ Mn and A ∈ Mn .
W. Cheung
semanticscholar +1 more source
Structured pseudospectra and the condition of a nonderogatory eigenvalue [PDF]
, 2010 Let $\lambda$ be a nonderogatory eigenvalue of $A\in\mathbb{C}^{n\times n}$ of algebraic multiplicity m. The sensitivity of $\lambda$ with respect to matrix perturbations of the form $A\leadsto A+\Delta$, $\Delta\in\boldsymbol{\Delta}$, is measured by ...
Karow, Michael
core +1 more source
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
core +3 more sources
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
core +1 more source
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
core
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
core +2 more sources
On the correlation function of the characteristic polynomials of the hermitian Wigner ensemble
, 2010 We consider the asymptotics of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}W_n$. We show that for the correlation function of any even order the asymptotic coincides with this for the GUE up ...
E. Brezin +12 more
core +1 more source