Hi there,

Please help. I was testing calculation of eigenvectors/eigenvalues of a 3x3 hermitian matrx with ZHEEV and got this strange error: all three eigenvectors are OK, but one eigenvalue is WRONG! 
What is going on here?
Here is short Fortran code and the result.

!===============================
program simpeMeig
IMPLICIT NONE
INTEGER :: N, LWORK, LDA, info
COMPLEX*16, DIMENSION(3,3) :: MTR, MATRIX
COMPLEX*16, DIMENSION(3) :: WORK
DOUBLE PRECISION, DIMENSION(3) :: W ! eigenvalues
DOUBLE PRECISION, DIMENSION(7):: RWORK
N=3
LDA=3
LWORK=5

! first row:
MTR(1,1) = 1
MTR(1,2) = 1
MTR(1,3) = 3
! second row:
MTR(2,1) = 1
MTR(2,2) = 1
MTR(2,3) = -3
! second row:
MTR(3,1) = 3
MTR(3,2) = -3
MTR(3,3) = -3
MATRIX(:,:) =MTR(:,:)
PRINT *, MTR(1,:)
PRINT *, MTR(2,:)
PRINT *, MTR(3,:)
CALL zheev('V', 'U', N, MATRIX, LDA, W, WORK, LWORK, RWORK, info)
print *,
print *, "INFO = ", info
print *,
print *, "First eigenvalue and eigenvector:"
print *, W(1)
print *, MATRIX(:,1)
print *,
print *, "Second eigenvalue and eigenvector:"
print *, W(2)
print *, MATRIX(:,2)
print *,
print *, "Third eigenvalue and eigenvector:"
print *, W(3)
print *, MATRIX(:,3)
print *, "========================================================="
end program simpeMeig

Result:
 =========================================================
 INFO =            0
 First eigenvalue and eigenvector:
  -6.0000000000000000     
 (-0.40824829046386307     ,  0.0000000000000000     ) ( 0.40824829046386307     ,  0.0000000000000000     ) ( 0.81649658092772603     ,  0.0000000000000000     )
 Second eigenvalue and eigenvector:
   2.9999999999999996     
 ( 0.57735026918962584     ,  0.0000000000000000     ) (-0.57735026918962584     ,  0.0000000000000000     ) ( 0.57735026918962573     ,  0.0000000000000000     )
 Third eigenvalue and eigenvector:
   64.000000000000000     
 ( 0.70710678118654746     ,  0.0000000000000000     ) ( 0.70710678118654768     ,  0.0000000000000000     ) (  0.0000000000000000     ,  0.0000000000000000     )
 =========================================================

The third eigenvalue should be 3, and NOT 64.  Please help!
Thanks.