On the fragmental structures.
On the Frobenius condition number of positive definite matrices.
On the function .
On the Gaussian random matrix ensembles with additional symmetry conditions.
On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate
In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...
On the Genesis of the Middle Product in Grassmann's Extensive Algebra
On the geometry of conjugacy classes in classical groupes.
On the Geometry of Positive Maps in Matrix Algebras.
On the group inverse of linear combinations of two group invertible matrices.
On the Hölder continuity of matrix functions for normal matrices.
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 invariant factors of sums of integral matrices
On the inverse eigenvalue problems: the case of superstars.
On the inverse of the adjacency matrix of a graph
A real symmetric matrix G with zero diagonal encodes the adjacencies of the vertices of a graph G with weighted edges and no loops. A graph associated with a n × n non–singular matrix with zero entries on the diagonal such that all its (n − 1) × (n − 1) principal submatrices are singular is said to be a NSSD. We show that the class of NSSDs is closed under taking the inverse of G. We present results on the nullities of one– and two–vertex deleted subgraphs of a NSSD. It is shown that a necessary...
On the invertibility of a linear function on the quaternions.
On the norm of GCD and related matrices.
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 linear capacity of algebraic cones
We define the linear capacity of an algebraic cone, give basic properties of the notion and new formulations of certain known results of the Matrix Theory. We derive in an explicit way the formula for the linear capacity of an irreducible component of the zero cone of a quadratic form over an algebraically closed field. We also give a formula for the linear capacity of the cone over the conjugacy class of a “generic” non-nilpotent matrix.
On the linearized stability of age-structured multispecies populations.
On the lower bound of the spectral norm of symmetric random matrices with independent entries.