= Row rank
{title2=$\dim\operatorname{row}(A)$}
The <row rank> of a <matrix> is the dimension of the <vector space> spanned by its rows. <Elementary row operations> preserve this space; multiplication on the right by an <invertible matrix> preserves all <linear relations> among the rows. In <row echelon form> the nonzero rows are <linearly independent>, so the row rank is the number of pivots. The pivot columns are also <linearly independent> and span the <column space>, proving equality with the <column rank>.
Back to article page
