On the asymptotic distributions of certain functional of eigenvalues of correlation matrices
On the asymptotics of certain Wiener--Hopf-plus-Hankel determinants.
On the automorphisms of the spectral unit ball
Let Ω be the spectral unit ball of Mₙ(ℂ), that is, the set of n × n matrices with spectral radius less than 1. We are interested in classifying the automorphisms of Ω. We know that it is enough to consider the normalized automorphisms of Ω, that is, the automorphisms F satisfying F(0) = 0 and F'(0) = I, where I is the identity map on Mₙ(ℂ). The known normalized automorphisms are conjugations. Is every normalized automorphism a conjugation? We show that locally, in a neighborhood of a matrix with...
On the average growth of random Fibonacci sequences.
On the belonging of a perturbed vector to a subspace from a numerical view point.
On the binary system of factors of formal matrix rings
We investigate the formal matrix ring over defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.
On the bounds for the spectral and norms of the Khatri-Rao product of Cauchy-Hankel matrices.
On the bounds of Laplacian eigenvalues of -connected graphs
Let be the algebraic connectivity, and let be the Laplacian spectral radius of a -connected graph with vertices and edges. In this paper, we prove that with equality if and only if is the complete graph or . Moreover, if is non-regular, then where stands for the maximum degree of . Remark that in some cases, these two inequalities improve some previously known results.
On the Brualdi-Liu conjecture for the even permanent.
On the Burnside problem for semigroups of matrices in the (max, + ) algebra.
On the calculation of evolutionarily stable strategies.
On the cardinality of complex matrix scalings
We disprove a conjecture made by Rajesh Pereira and Joanna Boneng regarding the upper bound on the number of doubly quasi-stochastic scalings of an n × n positive definite matrix. In doing so, we arrive at the true upper bound for 3 × 3 real matrices, and demonstrate that there is no such bound when n ≥ 4.
On the Cayley Factorization of Calotte Conditions.
On the Cayley transform of positivity classes of matrices.
On the central coefficients of Bell matrices.
On the characteristic equation of Chebyshev matrices.
On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems.
On the class of square Petrie matrices induced by cyclic permutations.
On the Classification of Hermitian Forms.
On the codimension of the variety of symmetric matrices with multiple eigenvalues.