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.