# Finding a Gaussian Distribution to approximate a distribution with non-positive definite covariance matrix

We have got a Gaussian distribution covariance matrix(precision matrix) and the potential information, that is, if g is proportional to exp(-X'KX+h'X). However, K here is not positive definite. So we would like to have an approximation of this function.

Vectorizing K and h into one vector, we have want to project the current distribution to a distribution with positive definite K.

There is a conclusion that disregarding the h vector, the best projection will just be to change negative eigenvalues of K to be 0(with least squared sum for each elements on K). But the question is, will the h vector affect this result? Or we may just use the same h vector since they only manipulate the first order terms?

Thank you very much!

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