Sign patterns that require eventual positivity or require eventual nonnegativity.
Sign patterns that require or allow power-positivity.
Signatura of magic and Latin integer squares: isentropic clans and indexing
The 2010 study of the Shannon entropy of order nine Sudoku and Latin square matrices by Newton and DeSalvo [Proc. Roy. Soc. A 2010] is extended to natural magic and Latin squares up to order nine. We demonstrate that decimal and integer measures of the Singular Value sets, here named SV clans, are a powerful way of comparing different integer squares. Several complete sets of magic and Latin squares are included, including the order eight Franklin subset which is of direct relevance...
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 differences of powers of -matrices
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....
is not boundedly generated by elementary matrices: explicit proof.
Smallest singular value of sparse random matrices
We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances of the entries....
Solution of linear matrix equations in a *congruence class.
Solution of the problem of optimal diagonal scaling for quasi-real Hermitian positive-definite matrices.
Solving a family of permutation problems on 0-1 matrices
Solving Confluent Vandermonde Systems of Hermite Type.
Solving linear systems with a Levinson-like solver.
Solving systems of two–sided (max, min)–linear equations
A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
Some Basic Properties of Some Special Matrices. Part III
This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties.
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 commutators and an application to spectral variation.
Some inequalities for spectral variations.