I've been reading this article about the look-at function. I don't understand the part when they're trying to inverse the matrix N.
They say that R is orthogonal because all its row and column vectors are orthogonal unit vectors.
This means that for example
$[s_x, v_x, f_x, 0]^T * [s_x, v_x, f_x, 0]^T = 1$
$[s_x, v_x, f_x, 0]^T * [s_y, v_y, f_y, 0]^T = 0$,
but why? Could anyone explain it to me or give a hint about why it's true?
I guess I have found the solution: I can quite easily prove that $R^T*R=I$. So if I could prove that $R^T*R=I\Longrightarrow R*R^T=I$, then by definition R is orthogonal.
Is the following proof correct (I'm not really good at math)?
$ R^T*R=I \Longleftrightarrow R*(R^T*R)=R*(I) \Longleftrightarrow (R*R^T)*R=R \Longleftrightarrow R*R^T=I $