I know this is a iff condition,and the reverse is easy to prove.But I am having some difficulty to prove that all non negative definite matrices are variance covariance matrix.From what i have collected from wikipedia,I tried to prove it this way.
Let A be a non negative definite matrix.
Then A can be written as
A=BB^t,B^t is the tranpose of B.
=Var(BX),where X is a random variable whose variance-covariance matrix is identity matrix I.
But this method is not generalising the proof for any variance covariance matrix.So is this approach correct? Also is there any better way to solve this?
Re: How to prove a non negative definite matrix has to be a variance-covariance matri
The approach of proof I tried, only proves that a non negative definite matrix is a variance covariance matrix of a set of linear combinations of some random variable whose variance covariance matrix is the identity matrix.So is this not becoming a particular case?