With Qq,n the distribution of n minus the rank of a matrix Mn chosen uniformly from Mat(n, q), the collection of all n × n matrices over the finite field Fq of size q ≥ 2, and Qq the distributional limit of Qq,n as n→∞, we apply Stein’s method to prove the total variation bound 1 8qn+1 ≤ ||Qq,n −Qq||TV ≤ 3 qn+1 . In addition, we obtain similar sharp results for the rank distributions of symmetr...

The title compound, dirubidium dimanganese(II) tris-(tetra-oxo-molyb-date), Rb2Mn2(MoO4)3, was prepared by solid-state reactions. The structure can be described as being composed of MnO6 octa-hedra sharing corners with MoO4 tetra-hedra. The three-dimensional framework contains cavities in which the rubidium ions are located. The Rb(+) cations are within distorted nine- and 12-vertex polyhedra. ...

We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized c...