In linear algebra, vectors $ v_1, v_2... v_n $ form a basis for $ R^m $ when
- The vectors span $ R^m $. (in other words, the span of the vectors is $ R^m $)
- The vectors are linearly independent.
For a basis, it follows that n must be equal to m.
(Note that there can be more than one set of vectors that form a basis for the same space.)
