Covariance matrix singularity

[Elena]

Hello,

Could anyone explain, why the matrix of covariance becomes singular when the the number of parameters P is less then the number of samples N?

Thank you in advance,
Elena

[Dason]

Did you mean to say when P is greater than the number of samples?

[Elena]

I meant that we have a set of variables X1,... Xp and n samples for each variable. Then it says that when p>>n the covariance matrix will be singular. Why?