Okay, so then that hypothesis goes out the window.
Tell me, does it then make sense to instead say that if [itex] \left\{ v_i \right\}_{i=1}^d [/itex] span a d dimensional space, then for w a linear combo of the [itex] v_i [/itex] it follows that [itex] \left\{ v_i  w \right\} [/itex] span a d1 dimensional space?
