Anybody know how I can build a orthogonal base using only a vector? I have a vector in the form $v_1 = [a, b, -a, -b]$, where $a$ and $b$ are real numbers. I did try build in the "adhoc way" but, nothing, I only got two orthogonal vectors:
$v_1 = [a, b, -a, -b], \text{ } v_2 = [a, -b, a, -b]$
I need more two vectors to complete the orthogonal basis $\{v_1, v_2, v_3, v_4\}$. Anybody can help me?
Thanks...