I have an initial matrix X. We can assume each element to be gaussian random variable around some mean, this mean being different for each element. I use an indicator random variable matrix Y, such that $Y = \textbf{1}(X \ge 0)$, i.e. Y is a matrix made up of Random Variables.
Now I want to decompose it into eigen vector ($V$) and eigen value($\Lambda$) matrix. Does $V$ and/or $\Lambda$ follow any specific distribution? Or can I find the Expectation of $V$ and $\Lambda$ individually?
Context: I have many such Y's, and I take the mean of them and get an expression for E(Y), and equate the two (using law of large numbers). Now I want to do the same, but with $V$ and $\Lambda$ instead of $Y$.
Edit: Added context.