On the Cayley transform of positivity classes of matrices.
On the convergence theory of double -weak splittings of type II
Recently, Wang (2017) has introduced the -nonnegative double splitting using the notion of matrices that leave a cone invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for -weak regular and -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes...
On the derivatives of the Perron vector
On the effect of the perturbation of a nonnegative matrix on its Perron eigenvector
On the matrix form of Kronecker lemma
A matrix generalization of Kronecker's lemma is presented with assumptions that make it possible not only the unboundedness of the condition number considered by Anderson and Moore (1976) but also other sequences of real matrices, not necessarily monotone increasing, symmetric and nonnegative definite. A useful matrix decomposition and a well-known equivalent result about convergent series are used in this generalization.
On the matrix norm subordinate to the Hölder norm.
On the Maximum Eigenvalue of a Reducible Non-Negative Real Matrix.
On the Monotonity of Incomplete Factorization.
On the Nonnegativity of XX* and its Relevance in Econometrics.
On the partial ordering of almost definite matrices
On the R-Order of Coupled Sequences Arising in Single-Step Type Methods.
On the singular graph and the Weyr characteristic of an M-matrix.
On the span invariant for cubic similarity
Given a real n×n matrix A, we make some conjectures and prove partial results about the range of the function that maps the n-tuple x into the entrywise kth power of the n-tuple Ax. This is of interest in the study of the Jacobian Conjecture.
On the star partial ordering of normal matrices.
On the structure of positive maps between matrix algebras
The structure of the set of positive unital maps between M₂(ℂ) and Mₙ(ℂ) (n ≥ 3) is investigated. We proceed with the study of the "quantized" Choi matrix thus extending the methods of our previous paper [MM2]. In particular, we examine the quantized version of Størmer's extremality condition. Maps fulfilling this condition are characterized. To illustrate our approach, a careful analysis of Tang's maps is given.
On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices.
On weighted partial orderings on the set of rectangular complex matrices.
On -extremal non-regular graphs.
One-sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices.
Operator norms of words formed from positive-definite matrices.