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Say you have a square (variance)covariance matrix S

How would one go about working S^-1/2 (inverse of the principle square)?

Bearing in mind, I'm trying to understand a paper which states:

I = S^-1/2 such that I(transposed) * I = S^-1

I've tried multiple suggestions, such as:

However, none of them seem to hold true for the latter part of the what's stated on the paper.

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You can obtain the square root of a matrix M using the Cholesky Decomposition, M = LL'. Then compute the inverse of L.

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