Can I rebuild a NxN matrix if I know its Covariance Matrix? If so, how would I go upon it? is there a Matlab function to do so?
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If $C$ is a covariance-matrix, then it is the product of some matrix $M$ with its transpose $M^t$ : $ C = M^t * M $ .
Even more, $T^t$ can have as many columns as we like as long they are more than rows. So the space, spanned by the columns of $T^t$ is of arbitrary dimension.
In short: the decomposition of $C$ is non-unique; there are infinitely many solutions.