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Can anybody tell me how I can check collinearity in $\mathbb{R}³$ ? I have multiple points, which I need to check for collinearity. According to wiki, I can do this by looking at the rank of a matrix (if I write those points into the matrix columns). My problem is that these points are e.g. noisy and therefore never form an ideal line, although they are very close to form one. So I want to figure out if these points are very close to form a line and not actually form a perfect line. Does anybody has a hint?

Thanks in advance

Horsti

horsti
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  • search for : principal component analysis ; linear regression; singular value decomposition – user619894 Jun 02 '20 at 14:43
  • Yepp i've used the PCA so far to determine the direction of all three components. What exactly is your approach to solve my problem using pca? – horsti Jun 02 '20 at 19:48
  • The ratio between the eigenvalues is a good measure of how colinear the points are. – user619894 Jun 02 '20 at 20:54

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