A consideration on the generation of extremely ill-conditioned matrices

摘要

We investigate the upper bound of the condition number of an integer matrix A = a_(ij) with a_(ij)≤μ. Concerning this problem the absolute upper bound was given by Guggenheimer et al. However it is not known whether this upper bound is really attainable or not. In this paper we examine two problems; (i) the relation among two coefficients p_1 and p_(n-1) of the characteristic polynomial of AA~T and the upper bound of the condition number of A. and (ii) the attainable maximum condition number by very small matrices.