On the Rodman-Shalom conjecture regarding the Jordan form of completions of partial upper triangular matrices.
On the R-Order of Coupled Sequences Arising in Single-Step Type Methods.
On the second-order correlation function of the characteristic polynomial of a real symmetric Wigner matrix.
On the separation of eigenvalues by the permutation group
Let A be an invertible 3 × 3 complex matrix. It is shown that there is a 3 × 3 permutation matrix P such that the product PA has at least two distinct eigenvalues. The nilpotent complex n × n matrices A for which the products PA with all symmetric matrices P have a single spectrum are determined. It is shown that for a n × n complex matrix [...] there exists a permutation matrix P such that the product PA has at least two distinct eigenvalues.
On the Sharpness of Some Upper Bounds for the Spectral Radii of S.O.R. Iteration Matrices.
On the shortest lattice vectors in a three-dimensional translational (Bravais) lattice
On the signless Laplacian spectral characterization of the line graphs of -shape trees
A graph is determined by its signless Laplacian spectrum if no other non-isomorphic graph has the same signless Laplacian spectrum (simply is ). Let denote the -shape tree obtained by identifying the end vertices of three paths , and . We prove that its all line graphs except () are , and determine the graphs which have the same signless Laplacian spectrum as . Let be the maximum signless Laplacian eigenvalue of the graph . We give the limit of , too.
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.