This sounds like a common application, but I didn't find a discussion of it.(adsbygoogle = window.adsbygoogle || []).push({});

Simple case:

I have 30 experimental values, and I have the full covariance matrix for the measurements (they are correlated). I am now interested in the sum of the first 5 measured values, the sum of the following 5 measured values, and so on. In total I want 6 valuesand their covariance matrix. The diagonal entries of the covariance matrix are easy - just sum the corresponding 5x5 blocks along the diagonal of the original covariance matrix. Do I get the other entries also as sum of the corresponding 5x5 blocks? I would expect so but a confirmation would be nice.

General case:

More generally, if my transformed variables are a weighted sum of the original variables (weights are not negative), how do I get the off-diagonal elements of the covariance matrix? As long as two transformed variables do not share a common measured value, I can scale everything in the covariance matrix to get back to the previous case. But what if they do? I was playing around with rotation matrices (going to a basis of transformed variables plus some dummy variables) but somehow it didn't work, and constructing 30x30 rotation matrices is ugly.

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# A Covariance matrix for transformed variables

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