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.
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They say that R is orthogonal because all its row and column vectors are orthogonal unit vectors. enter image description here
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 $

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

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