The Principal Maxmin Matrix Transversal Strategy

Given a fully irreducible matrix Y, we present a new matrix transversal strategy for the finding of a permutation matrix Q such that the condition numbers of the leading block A and its Schur complement D − CA⁻¹B in a 2 × 2 block form of YQ are as small as possible with respect to the i_∞-norm. Our notion of principal maxmin transversal of a matrix is a special case of an important combinatorial mathematics notion introduced by P. Hall more than 40 years ago.