On the weight matrices of linear difference equations
On the Yang-Baxter-like matrix equation for rank-two matrices
Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.
On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix.
On traces of exterior powers of a sum of two endomorphisms of a projective module
On transformation semigroups which are -semigroups.
On tropical Kleene star matrices and alcoved polytopes
In this paper we give a short, elementary proof of a known result in tropical mathematics, by which the convexity of the column span of a zero-diagonal real matrix is characterized by being a Kleene star. We give applications to alcoved polytopes, using normal idempotent matrices (which form a subclass of Kleene stars). For a normal matrix we define a norm and show that this is the radius of a hyperplane section of its tropical span.
On two characteristic properties of Euclidean norms.
On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices.
On two matrix derivatives by Kollo and von Rosen.
The article establishes relationships between the matrix derivatives of F with respect to X as introduced by von Rosen (1988), Kollo and von Rosen (2000) and the Magnus-Neudecker (1999) matrix derivative. The usual transformations apply and the Moore-Penrose inverse of the duplication matrix is used. Both X and F have the same dimension.
On two-dimensional linear spaces of continuous functions of the same character
On uniform symmetrization of analytic matrix functions
On unimodular complements
On unit-regular ideals.
On upper triangular nonnegative matrices
We first investigate factorizations of elements of the semigroup of upper triangular matrices with nonnegative entries and nonzero determinant, provide a formula for , and, given , also provide formulas for , and . As a consequence, open problem 2 and problem 4 presented in N. Baeth et al. (2011), are partly answered. Secondly, we study the semigroup of upper triangular matrices with only positive integral entries, compute some invariants of such semigroup, and also partly answer open Problem...
On various dynamic compensations
On weak convergence of sequences of measures
On weakly positive unit forms.
On weighted partial orderings on the set of rectangular complex matrices.
On -extremal non-regular graphs.
One-sided complements and solutions of the equation in semirings.