Repeated eigenvalues

If a matrix has repeated eigenvalues, the eigenvectors of the matched repeated eigenvalues become one of eigenspace. For example, the identity matrix has all repeated eigenvalues of one. The eigenvectors of the identity matrix are any vectors of the whole column space of the identity matrix. The whole column space is the eigenspace. A symmetric matrix can be chosen with orthogonal eigenvectors not only orthogonal eigenvectors because when a symmetric matrix has repeated eigenvalues, the eigenvectors that correspond to the repeated eigenvalues do not have to be orthonormal but can be orthonormal.