Covariance matrix

Hi,

I was going through the course again, and I was wondering why the covariance matrix is positive semi-definite and not positive definite.

Wouldn't there be problems if one or more of the eigenvalues were zero? Especially for inversion?

cov.jpg

I don't know to be honest, but it does not seem like a mistake as I've searched for it online and the same conclusion about the covariance matrix seem to pop up.

Any student that knows ?

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