I am studying data analysis and especially PCA (principal component analysis) and reviewing the very course i took a few years ago, i found a result that seems interesting but there is no proof and i can't find it myself.
Here is a capture of the slide :
(yeah i'm french), so, as far as i understood it, $\theta$ is the angle between the vector defined by the data point $e_i$ and the projection plane. I guess it is useful to measure the quality of the representation of the data, the thing is i couldn't prove this result myself.
What am i missing ?
Thank you for your help.
These are direction cosines.Note that $ O f e_1 $ is a right angle.$\theta$ is angle of elevation.
$$ \frac{x^2 + y^2 + z^2}{L^2} =1 $$
$$ \cos^2 \theta_1 +\cos^2 \theta_2 +\cos^2 \theta_3 = l^2+m^2+n^2 =1 $$
$$ \cos^2 \theta = \frac{x^2 + y^2 }{L^2}. $$