On the structure of nilpotent endomorphisms and applications.
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 the subspace of .
On the symmetry classes of the first covariant derivatives of tensor fields.
On the symplectic structure of irreducible representation modules of the metacyclic group . (Zur symplektischen Struktur irreduzibler Darstellungsmoduln der metazyklischen Gruppe .)
On the trace characterization of the joint spectral radius.
On the vectors associated with the roots of max-plus characteristic polynomials
We discuss the eigenvalue problem in the max-plus algebra. For a max-plus square matrix, the roots of its characteristic polynomial are not its eigenvalues. In this paper, we give the notion of algebraic eigenvectors associated with the roots of characteristic polynomials. Algebraic eigenvectors are the analogues of the usual eigenvectors in the following three senses: (1) An algebraic eigenvector satisfies an equation similar to the equation for usual eigenvectors. Under a suitable assumption,...
On the volume of the double stochastic matrices.
On the volume of the polytope of doubly stochastic matrices.
On the weak robustness of fuzzy matrices
A matrix in -algebra (fuzzy matrix) is called weakly robust if is an eigenvector of only if is an eigenvector of . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an algorithm for checking the weak robustness is described.
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