[Math] Confusion over the usage of different terms for ref and rref.

linear algebraterminology

My school uses row echelon form and reduced row echelon form to denote their respective types of matrices which results from gauss jordan elimination.

Today I came across this term used in this sentence.

The nonzero rows of a row reduced echelon matrix form a basis for the row space of the matrix.

The nonzero rows of a row reduced echelon matrix are independent.

http://www.millersville.edu/~bikenaga/linear-algebra/rank/rank.html

I am confused about the term "row reduced echelon". Which is it referring to?

Also I would like to clarify if,

The nonzero rows of a Row Echelon Form matrix form a basis for the row space of the matrix. (i.e non RREF)

Best Answer

Row reduced echelon is the same thing as reduced row echelon form (although admittedly, the terminology is a bit weird). The rows of the row echelon form does indeed form a basis for the row space.