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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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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The difference and sum of projectors [PDF]
, 2004 The aim of this paper is to present new results on the invertibility of the sum of projectors, and new relations between the nonsingularity of the difference and the sum of projectors. We also give simple proofs, without referring to rank theory, of some
Koliha, J.J +2 more
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Characterizations of inverse M-matrices with special zero patterns [PDF]
, 2010 In this paper, we provide some characterizations of inverse M-matrices with special zero patterns. In particular, we give necessary and sufficient conditions for k-diagonal matrices and symmetric k-diagonal matrices to be inverse M-matrices. In addition,
Huang, Rong +2 more
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On matrices whose nontrivial real linear combinations are nonsingular.
, 1971 Let F be the real field R, the complex field C, or the skew field H of quaternions, and d(F) the real dimension of F. We shall write F(n) (resp. Fz(n)) for the maximum number of nXn matrices (resp.
Yik-Hoi Au-Yeung
semanticscholar +1 more source
A dominance theorem for partitioned Hermitian matrices
, 1972 Let A = (Atl) be a partitioned positive semidefinite hermitian matrix, where An is «-square, 1 tsi,j=m. A class of ordered pairs of functions (/i,/a) is given such that (fi(Ati)) — (f2(Ati)) is positive semidefinite hermitian. Applications are given.
R. Merris
semanticscholar +1 more source
Reduction of the pseudoinverse of a Hermitian persymmetric matrix
, 1974 When the pseudoinverse of a Hermitian persymmetric matrix is computed, both computer time and storage can be reduced by taking advantage of the special structure of the matrix. For any matrix M, let M' and M* denote its transpose and conjugate transpose,
M. Goldstein
semanticscholar +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
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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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
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