Column-partitioned matrices over rings without invertible transversal submatrices

Stephan Foldes, Erkko Lehtonen

Research output: Contribution to journalArticlepeer-review


Let the columns of a p x 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.

Original languageBritish English
Pages (from-to)33-39
Number of pages7
JournalArs Combinatoria
StatePublished - Oct 2010


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