by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

Two Hadamard matrices are considered equivalent if one is obtained from the other by a sequence of operations involving row or column permutations or negations. We complete the classification of Hadamard matrices of order 32. It turns out that there are exactly 13710027 such matrices up to equivalence. AMS Subject Classification: 05B20, 05B05, 05B30.

Some large rectangular matrices used in animal breeding are presented. We describe how to generate these matrices from the data supplied by animal breeders. The matrices are very sparse (3 nonzeros per row) and range between 26 20 and 968 652 582 694.

In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m× n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied.

This paper presents a new technique for computing the barycenter of a set of distance or kernel matrices. These matrices, which define the interrelationships between points sampled from individual domains, are not required to have the same size or to be in row-by-row correspondence. We compare these matrices using the softassign criterion, which measures the minimum distortion induced by a prob...

The matrix chain ordering problem is to find the cheapest way to multiply a chain of n matrices, where the matrices are pairwise compatible but of varying dimensions. Here we give several new parallel algorithms including O(lg3 n)-time and n/lgn-processor algorithms for solving the matrix chain ordering problem and for solving an optimal triangulation problem of convex polygons on the common CR...

In order to efficiently compute some combinatorial designs based upon circulant matrices which have different, defined numbers of 1's and 0's in each row and column we need to find candidate vectors with differing weights and Hamming distances. This paper concentrates on how to efficiently create such circulant matrices. These circulant matrices have applications in signal processing, public ke...

Two opposing patterns of meta-community organization are nestedness and negative species co-occurrence. Both patterns can be quantified with metrics that are applied to presence-absence matrices and tested with null model analysis. Previous meta-analyses have given conflicting results, with the same set of matrices apparently showing high nestedness (Wright et al. 1998) and negative species co-...

Consider an invertible n × n matrix over some field. The Gauss-Jordan elimination reduces this matrix to the identity matrix using at most n row operations and in general that many operations might be needed. In [1] the authors considered matrices in GL(n, q), the set of n × n invertible matrices in the finite field of q elements, and provided an algorithm using only row operations which perfor...