On a class of matrices which arise in the numerical solution of Euler equations.
On a classic example in the nonnegative inverse eigenvalue problem.
On a geometric property of positive definite matrices cone.
On a nonnegative irreducible matrix that is similar to a positive matrix
Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.
On a Schur complement inequality for the Hadamard product of certain totally nonnegative matrices.
On a strong form of a conjecture of Boyle and Handelman.
On Bauer's Generalized Gershgorin Discs.
On (con)similarities and congruences between and , or .
On Exponents of Primitive Matrices.
On Fixed Point Linear Equations.
On general matrices having the Perron-Frobenius property.
On linear maps leaving invariant the copositive/completely positive cones
The objective of this manuscript is to investigate the structure of linear maps on the space of real symmetric matrices that leave invariant the closed convex cones of copositive and completely positive matrices ( and ). A description of an invertible linear map on such that is obtained in terms of semipositive maps over the positive semidefinite cone and the cone of symmetric nonnegative matrices for , with specific calculations for . Preserver properties of the Lyapunov map , the...
On matrices having an invariant cone
On matrices with all minors negative.
On means of positive definite matrices
On nonnegative matrices with given row and column sums.
On nonnegative operators and fully cyclic peripheral spectrum.
On nonnegative sign equivalent and sign similar factorizations of matrices.
On orderings induced by the Loewner partial ordering
The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.
On Powers of Non-Negative Matrices