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Correntropy relationship to linearity and matrix values

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I am only somewhat familiar with the subject, but I will an attempt to answer your questions as best as I'm able.

1. A very simply measure of similarity between two random variables X and Y would be the covariance, i.e.
Cov[X,Y]. An feature of this measure is that it is (bi-)linear, i.e. for random variables X, Y, Z, and real number a,

         Cov(X+aY, Z) = Cov(X, Z) + aCov(Y,Z).
 The correntropy of two random variables X and Y is
   
         Correntropy(X,Y) = E[K(X-Y)]
where K is a kernel function. This measure generally isn't linear.
2. Yeah, it seems the values should range from a11 to a1m (a21 to a2m). Looks like a typo.
3. No idea, sorry.

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