why one of eigen values of a covariance matrix is zero? let say you have a square matrix A, you calculate covariance of it, then calculate eigenvalues and eigen vectors. It follows that one of eigen values is equal to zero. why is it so? what does it mean in terms of interpretation of eigen vectors?
Thanks

It is because $n$ points in $n$-dimensional space are always situated on a codimension (at least) one affine subspace. The variance in a orthogonal direction to this subspace will be zero and this variance is expressed by an eigenvalue of the covariance matrix of these $n$ points.
