Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I got stuck with the following problem:

Let X, Y and Z be three random vectors of the same length drawn from a continuous random distribution.

where

Z is independent of X and Y but [itex]Y=f(X)[/itex] with a non-linear function [itex]f[/itex].

Can I claim that:

1. [itex]Z^{T}X\neq 0[/itex] almost surely (i.e., vector X wouldn't almost surely lay on the null space of vector Z),

or

2. [itex]Y^{T}X= 0[/itex] almost surely (i.e., vector X would almost surely lay on the null space of vector Y).

If so, could you give me a hint to the proof or a citation.

Thank you for your help in advance.

Hussein

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# Two independent random vectors are almost surely non-orthogonal

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