minimal covariance maximal variance

Hello,

I'm working on a datapreprocessing method which results in a large number of variables (eg. 500, same unit) for a number of cases N. In the ideal case each variable would show a large variance but the correlation/covariance between separate variables would be zero.

Does anyone now of a statistic which measures this? As a heuristic I could take for example the mean covariance / mean variance ratio which should be minimal, but I think there should be a more appropriate measure.

Thanks a lot!
Tim
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