# Does this matrix normal form have a name and has it been used?

In a research paper in Theoretical Computer Science, we are using a certain matrix normal form, which I was not able to find in the literature (I have to admit that my Linear Algebra got a bit rusty, since I graduated). This normal form can be considered as a relaxed version of reduced Row Echelon Form which is defined as follows (quotation from Wikipedia): " - All nonzero rows are above any rows of all zeroes. - The leading coefficient of a nonzero row is always strictly to the right of the leading coefficient of the row above it. - Every leading coefficient is 1 and is the only nonzero entry in its column."

The relaxation is that we do not require that the leading coefficient of a nonzero row needs to be the only nonzero entry in its column. We only require that some nonzero coefficient of each nonzero row is the only nonzero entry in its column. I would be grateful for any pointers to the literature regarding this normal form or any normal form "between" reduced Row Echelon Form and "ours".