On the singular decomposition of matrices.
On the singular graph and the Weyr characteristic of an M-matrix.
On the singular two-parameter eigenvalue problem.
On the singular values of random matrices
We present an approach that allows one to bound the largest and smallest singular values of an random matrix with iid rows, distributed according to a measure on that is supported in a relatively small ball and linear functionals are uniformly bounded in for some , in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of not only in the case of the above mentioned measure, but also when the measure is log-concave or when it a product measure...
On the Singularities of Functions with Values in a Clifford Algebra.
On the solution of multiparameter problems of algebra. IV: The algorithm and its applications.
On the solution of multiparameter problems of algebra. V: The - factorization algorithm and its applications.
On the Solution of sigma-alpha Regular Generalized Linear Systems
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 special trace decomposition problem on quaternion structure.
On the spectral norm of a random Toeplitz matrix.
On the star partial ordering of normal matrices.
On the strong Arnol'd hypothesis and the connectivity of graphs.
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,...