When minimizing by real number q a value of lost function L=(A-qB)^2/A^2 with the A as the reference vector we receive Lmin=(1-(AB)^2/A2*B^2) where X^2=X1^2+...Xn^2, XY=X1Y1+...XnYn. Physical sense of the Lmin is sin^2(fi) where the fi is nD-angle between the vectors A and B. Supposing normal distribution for all components of both vectors what is distribution law for the sin^2(fi)?
At least what is the distribution law for the sin^2(fi) for two velocity vectors of molecules in Maxwell gas (n=3)?
"Atomic" solution for the ratios Bi/Ai,...Ai/sqrt(A^2) etc is not acceptable.
See these links:
https://doi.org/10.1111/j.1600-0587.2012.07348.x
https://www.listendata.com/2015/04/detecting-multicollinearity-in-categorical-variables.html
Thank You Remal for Your information but my problem is more simple: how to prove that two vectors with noised coordinates are collinear at conf.level P=0.95.
Kind tegards
Viktor
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