The quaternion matrix-valued Young's inequality.
The quaternionic determinant.
The random paving property for uniformly bounded matrices
This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original proof of...
The rank of the difference of similar matrices
The rate of convergence for spectra of GUE and LUE matrix ensembles
We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.
The reciprocal super Catalan matrix
The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.
The reflexive re-nonnegative definite solution to a quaternion matrix equation.
The restricted Toda chain, exponential Riordan arrays, and Hankel transforms.
The semigroup of circulant Boolean matrices
The semigroup of fully indecomposable relations and Hall relations
The Similarity Reduction of Matrices over a Skew Field.
The Smith normal form of product distance matrices
Let G = (V, E) be a connected graph with 2-connected blocks H1, H2, . . . , Hr. Motivated by the exponential distance matrix, Bapat and Sivasubramanian in [4] defined its product distance matrix DG and showed that det DG only depends on det DHi for 1 ≤ i ≤ r and not on the manner in which its blocks are connected. In this work, when distances are symmetric, we generalize this result to the Smith Normal Form of DG and give an explicit formula for the invariant factors of DG.
The special circulant matrix and units in group rings.
The spectral gap of random graphs with given expected degrees.
The spectral laws of Hermitian block-matrices with large random blocks.
The spectrum of coupled random matrices.
The Spectrum of Jacobi Matrices.
The structure of linear operators strongly preserving majorizations of matrices.
The structure of linear preservers of left matrix majorization on .
The structured distance to nearly normal matrices.