# Help with understanding the look-at function (the view matrix)

They say that R is orthogonal because all its row and column vectors are orthogonal unit vectors.
This means that for example

$$[s_x, v_x, f_x, 0]^T * [s_x, v_x, f_x, 0]^T = 1$$

or

$$[s_x, v_x, f_x, 0]^T * [s_y, v_y, f_y, 0]^T = 0$$,

but why? Could anyone explain it to me or give a hint about why it's true?

EDIT:
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)?
$$R^T*R=I \Longleftrightarrow R*(R^T*R)=R*(I) \Longleftrightarrow (R*R^T)*R=R \Longleftrightarrow R*R^T=I$$

• Because it is a rotation matrix. Look up the SO(3) group. – lightxbulb Aug 15 '19 at 9:05