On the permanents of certain circulant matrices and related Toeplitz matrices. (Über die Permanente gewisser zirkulanter Matrizen und damit zusammenhängender Toeplitz-Matrizen.)
On the perturbation of Markov chains with nearly transient states.
On the polynomial numerical hull of a normal matrix.
On the Prime Ideal of an Ordering of Higher Level.
On the principal minors of a matrix with a multiple eigenvalue.
On the problem in max algebra: every system of intervals is a spectrum
We consider the two-sided eigenproblem over max algebra. It is shown that any finite system of real intervals and points can be represented as spectrum of this eigenproblem.
On the pseudoinverse of a sum of symmetric matrices with applications to estimation
On the reduction of a Hamiltonian matrix to Hamiltonian Schur form.
On the reduction of a random basis
For p ≤ n, let b1(n),...,bp(n) be independent random vectors in with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...
On the reflexivity of multigenerator algebras [Book]
On the relation between Moore's and Penrose's conditions.
On the relation between the numerical range and the joint numerical range of matrix polynomials.
On the Relationships between Zero Forcing Numbers and Certain Graph Coverings
The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all the vertices of the graph, while the positive zero forcing number is an upper bound on the minimum number of induced trees in the graph needed to cover all the vertices in the graph. We show that for a block-cycle graph the zero forcing number equals...
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 and normalized signless Laplacian spreads of graphs
Let , , be a simple connected graph with vertices, edges and a sequence of vertex degrees . Denote by and the adjacency matrix and diagonal vertex degree matrix of , respectively. The signless Laplacian of is defined as and the normalized signless Laplacian matrix as . The normalized signless Laplacian spreads of a connected nonbipartite graph are defined as and , where are eigenvalues of . We establish sharp lower and upper bounds for the normalized signless Laplacian spreads...