On the second-order correlation function of the characteristic polynomial of a real symmetric Wigner matrix.
On the Sharpness of Some Upper Bounds for the Spectral Radii of S.O.R. Iteration Matrices.
On the singular graph and the Weyr characteristic of an M-matrix.
On the singular values of random matrices
We present an approach that allows one to bound the largest and smallest singular values of an random matrix with iid rows, distributed according to a measure on that is supported in a relatively small ball and linear functionals are uniformly bounded in for some , in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of not only in the case of the above mentioned measure, but also when the measure is log-concave or when it a product measure...
On the span invariant for cubic similarity
Given a real n×n matrix A, we make some conjectures and prove partial results about the range of the function that maps the n-tuple x into the entrywise kth power of the n-tuple Ax. This is of interest in the study of the Jacobian Conjecture.
On the special trace decomposition problem on quaternion structure.
On the spectral norm of a random Toeplitz matrix.
On the star partial ordering of normal matrices.
On the structure of positive maps between matrix algebras
The structure of the set of positive unital maps between M₂(ℂ) and Mₙ(ℂ) (n ≥ 3) is investigated. We proceed with the study of the "quantized" Choi matrix thus extending the methods of our previous paper [MM2]. In particular, we examine the quantized version of Størmer's extremality condition. Maps fulfilling this condition are characterized. To illustrate our approach, a careful analysis of Tang's maps is given.
On the volume of the double stochastic matrices.
On the volume of the polytope of doubly stochastic matrices.
On the weak robustness of fuzzy matrices
A matrix in -algebra (fuzzy matrix) is called weakly robust if is an eigenvector of only if is an eigenvector of . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an algorithm for checking the weak robustness is described.
On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix.
On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices.
On unimodular complements
On various dynamic compensations
On weak convergence of sequences of measures
On weighted partial orderings on the set of rectangular complex matrices.
On -extremal non-regular graphs.
One-sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices.