On the codimension of the variety of symmetric matrices with multiple eigenvalues.
On the derivatives of the Perron vector
On The Determinant of q-Distance Matrix of a Graph
In this note, we show how the determinant of the q-distance matrix Dq(T) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph...
On the effect of the perturbation of a nonnegative matrix on its Perron eigenvector
On the Effective Computation of the Inertia of a Non-Hermitian Matrix.
On the Eigenvalues of some Class of Pseudo-linear Transformations
On the Eigenvalues of Sums of Hermitian Matrices. II.
On the eigenvalues which express antieigenvalues.
On the estrada index of graphs with given number of cut edges.
On the first eigenvalue of bipartite graphs.
On the inertia sets of some symmetric sign patterns
A matrix whose entries consist of elements from the set is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices.
On the inverse eigenvalue problems: the case of superstars.
On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution
We consider n × n real symmetric and hermitian random matrices Hₙ that are sums of a non-random matrix and of mₙ rank-one matrices determined by i.i.d. isotropic random vectors with log-concave probability law and real amplitudes. This is an analog of the setting of Marchenko and Pastur [Mat. Sb. 72 (1967)]. We prove that if mₙ/n → c ∈ [0,∞) as n → ∞, and the distribution of eigenvalues of and the distribution of amplitudes converge weakly, then the distribution of eigenvalues of Hₙ converges...
On the lower bound of the spectral norm of symmetric random matrices with independent entries.
On the -th roots of a complex matrix.
On the matrices of central linear mappings
We show that a central linear mapping of a projectively embedded Euclidean -space onto a projectively embedded Euclidean -space is decomposable into a central projection followed by a similarity if, and only if, the least singular value of a certain matrix has multiplicity . This matrix is arising, by a simple manipulation, from a matrix describing the given mapping in terms of homogeneous Cartesian coordinates.
On the matrix norm subordinate to the Hölder norm.
On the Maximum Eigenvalue of a Reducible Non-Negative Real Matrix.
On the maximum positive semi-definite nullity and the cycle matroid of graphs.
On the minimum rank of not necessarily symmetric matrices: a preliminary study.