 This is especially important if and are Hermitian matrices, since in this case is not generally Hermitian and important properties of the solution are no longer apparent.If and are both symmetric or Hermitian, and is also a positive-definite matrix, the eigenvalues are real and eigenvectors and with distinct eigenvalues are -orthogonal ().In this case, eigenvectors can be chosen so that the matrix 
defined above satisfies

and there exists a basis of generalized eigenvectors (it is not a defective problem).