For a covariance matrix, what would be the properties associated with the eigenvectors space of this matrix? I want to know, since the covariance matrix is symmetric, positive, and semi-definite, then if I calculate its eigenvectors what would be the properties of the space constructed by those eigenvectors (corresponds to non-close-zero eigenvalues), is it orthogonal or anything else special?
Suppose this eigenvector matrix is called U, then what would be the properties with
U*transpose(U)？

The eigenvectors correspond to the principal components and the eigenvalues correspond to the variance explained by the principal components. 
