Defactoring: Difference between revisions

The most general form, with the fewest constraints, is simply called '''[https://en.wikipedia.org/wiki/Row_echelon_form Row Echelon Form]''', or '''REF'''. Its only constraint is ''echelon<ref>The name "echelon" is a French word for a military troop formation with a similar triangular shape.</ref> form'': each row's pivot, or first nonzero entry, is strictly to the right of the preceding row's pivot. This single constraint is fairly weak, and therefore REF does not produce a unique representation. This constraint is shared by every matrix form discussed here.

'''[https://people.sc.fsu.edu/~jburkardt/f_src/row_echelon_integer/row_echelon_integer.html Integer Row Echelon Form]''', or '''IREF''', is, unsurprisingly, any REF which meets an additional ''integer'' constraint, or in other words, that all of its entries are integers. This is still not a sufficiently strict set of constraints to ensure a unique representation.