When [math]u[/math] is in null space of [math]M[/math], [math]Mu=0[/math], which implies that [math]w'=Mv[/math], meaning that [math]w'[/math] depends only on [math]v[/math]. Geometrically, as [math]w[/math] moves along the dotted line on the left, [math]w'[/math] stays fixed on the right. [br][br]When [math]u[/math] is in [b]not[/b] in the null space of [math]M[/math], as [math]w[/math] moves along the dotted line on the left, [math]w'[/math] moves along a line parallel to [math]u'[/math].