The similarity class of a matrix Original Research Article

If A is an n × n matrix over an infinite field F, k is a positive integer, and R is an arbitrary n × k matrix image over the field F, where R2 is a nonsingular k × k matrix, we give a necessary and sufficient condition which guarantees that the similarity class of A contains [R, S] for some n × (n − k) matrix S over the field F. This result extends a result of Barría and Halmos.