To start with (and to use this nice LATEX tool) what do we have:
A time dependent vector:
And we define the expected value operator <> which means averaging over time.
The question is what is represented by the following two expressions.
No, in this case the T's cannot just be ignored as I would usually do.
The first one is a matrix like
is a matrix.
The covariance matrix, in other words:
The second expression is a number, the sum of all the variances or the trace of the covariance matrix (which stays invariant with a similarity transformation).
As far as implementation goes, I can only stress how nice numpy is. All I had to do was the parsing. Numpy quietly converts my 66x19553 matrix into its covariance matrix and diagonalises it.
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