-matrices and Lyapunov scalar stability.
Path product and inverse M-matrices.
Paths of matrices with the strong Perron-Frobenius property converging to a given matrix with the Perron-Frobenius property.
Perron complements of diagonally dominant matrices and H-matrices.
Perturbing non-real eigenvalues of nonnegative real matrices.
Positive 2D discrete-time linear Lyapunov systems
Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
Positive semidefinite matrices, exponential convexity for majorization, and related Cauchy means.
Positive splittings of matrices and their nonnegative Moore-Penrose inverses
In this short note we study necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a real matrix in terms of certain spectral property shared by all positive splittings of the given matrix.
Positivity and stabilization of 2D linear systems
The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.
Positivity in Complex Spaces and Its Application to Gershgorin Discs.
Positivity with Respect to the Round Cone
Products of Infinite-Dimensional Non-Negative Matrices; Extension of Hajnal's Results.
Products of -matrices and nested sequences of principal minors.
Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem.
Quadratic forms and Azumaya algebras.
Quelques généralisations du 17e problème de Hilbert.
Ranks of permutative matrices
A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.
Reachability indices of positive linear systems.
Reachability of cone fractional continuous-time linear systems
A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.
Recherche de la dimension de l'espace latent en ACP