Column-partitioned matrices over rings without invertible transversal submatrices

Abstract:  Let the columns of a p×q matrix M over any ring be partitioned into n blocks, M = [M1,...,Mn]. If no p×p submatrix of M with columns from distinct blocks Mi is invertible, then there is an invertible p×p matrix Q and a positive integer m ≤ p such that QM = [QM1,...,QMn] is in reduced echelon form and in all but at most m - 1 blocks QMi the last m entries of each column are either all zero or they include a non-zero non-unit.

Publication Year:   2010

Research Unit:   University of Luxembourg, FSTC, CSC

Reference:  Ars Combinatoria, 97 (2010), pp. 33-39