Recognition of hidden positive row diagonally dominant matrices.
Regions containing eigenvalues of a matrix.
Reverses of the Golden-Thompson type inequalities due to Ando-Hiai-Petz.
Robust stability of positive continuous-time linear systems with delays
The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.
Schur multiplier characterization of a class of infinite matrices
Let denote the space of infinite matrices for which for all with . We characterize the upper triangular positive matrices from , , by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.
Semigroups of finite matrices.
Several matrix Euclidean norm inequalities involving Kantorovich inequality.
Sign patterns that allow eventual positivity.
Sign patterns that require a positive or nonnegative left inverse.
Sign patterns that require eventual positivity or require eventual nonnegativity.
Sign patterns that require or allow power-positivity.
Simple conditions for practical stability of positive fractional discrete-time linear systems
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical...
Singular M-matrices which may not have a nonnegative generalized inverse
A matrix A ∈ ℝn×n is a GM-matrix if A = sI − B, where 0 < ρ(B) ≤ s and B ∈WPFn i.e., both B and Bt have ρ(B) as their eigenvalues and their corresponding eigenvector is entry wise nonnegative. In this article, we consider a generalization of a subclass of GM-matrices having a nonnegative core nilpotent decomposition and prove a characterization result for such matrices. Also, we study various notions of splitting of matrices from this new class and obtain sufficient conditions for their convergence....
Solution of linear matrix equations in a *congruence class.
Some bounds for the spectral radius of the Hadamard product of matrices.
Some characterizations of totally nonpositive (totally negative) matrices.
Some estimates in the theory of non-negative matrices
Some inequalities for sums of nonnegative definite matrices in quaternions.
Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix
Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.
Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse.