In the special case that is a normal matrix, which by definition must be square, the spectral theorem says that it can be unitarily diagonalized using a basis of eigenvectors, so that it can be written for a unitary matrix and a diagonal matrix . When is also positive semi-definite, the decomposition is also a singular value decomposition. Otherwise, it can be recast as an SVD by moving the phase of each to either its corresponding or . The natural connection of the SVD to non-normal matrices is through the polar decomposition theorem: , where is positive semidefinite and normal, and is unitary.