Definition:Row Equivalence

Definition
Two matrices $\mathbf A = \left[{a}\right]_{m n}, \mathbf B = \left[{b}\right]_{m n}$ are row equivalent if one can be obtained from the other by a finite sequence of elementary row operations.

This relationship is sometimes denoted $\mathbf{A} \sim \mathbf{B}$.

Also see

 * Row Equivalence is Equivalence Relation