A Note on Extreme Positive Definite Matrices.
A note on generalized Perron complements of -matrices.
A note on Newton and Newton-like inequalities for -matrices and for Drazin inverses of -matrices.
A note on nonnegative matrices
A note on regularity and positive definiteness of interval matrices
We present a sufficient regularity condition for interval matrices which generalizes two previously known ones. It is formulated in terms of positive definiteness of a certain point matrix, and can also be used for checking positive definiteness of interval matrices. Comparing it with Beeck’s strong regularity condition, we show by counterexamples that none of the two conditions is more general than the other one.
A note on the cp-rank of matrices generated by Soules matrices.
A p-adic Perron-Frobenius theorem
We prove that if an n×n matrix defined over ℚ ₚ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ℚ ₚ, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a p-adic analogue of the Perron-Frobenius theorem for positive real matrices.
A polynomial time spectra decomposition test for certain classes of inverse M-matrices.
A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory
A refinement of an inequality of Johnson, Loewy and London on nonnegative matrices and some applications.
A semigroup treatment of some theorems on non-negative matrices
A sparsity result on nonnegative real matrices with given spectrum
Let σ=(λ1,...,λn) be the spectrum of a nonnegative real n × n matrix. It is shown that σ is the spectrum of a nonnegative real n × n matrix having at most nonzero entries.
A trace inequality for positive definite matrices.
Algorithmes tronques de découpe linéaire
Alternating projected Barzilai-Borwein methods for nonnegative matrix factorization.
An algorithm for determining if the inverse of a strictly diagonally dominant Stieltjes matrix is strictly ultrametric.
An Example on Strong Equivalence of Positive Integral Matrices.
An explicit factorization of totally positive generalized Vandermonde matrices avoiding Schur functions.
An improved characterisation of the interior of the completely positive cone.
An improvement of an inequality of Fiedler leading to a new conjecture on nonnegative matrices
Suppose that is an nonnegative matrix whose eigenvalues are . Fiedler and others have shown that , for all , with equality for any such if and only if is the simple cycle matrix. Let be the signed sum of the determinants of the principal submatrices of of order , . We use similar techniques to Fiedler to show that Fiedler’s inequality can be strengthened to: , for all . We use this inequality to derive the inequality that: . In the spirit of a celebrated conjecture due to Boyle-Handelman,...