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Eigenvalues of Hermitean
Orthogonality of Eigenvectors of Hermitean Matrices
Now take any two eigenvectors/values
Take complex conjugate of this equation
Subtract
and
either
or
so eigenvectors of different eigenvalues are orthogonal.
Note if
and
are distinct eigenvectors of same degenerate eigenvalue
, then we can replace
by
where
is a linear combination of
and
, and
.
Geoffrey Fox
,
Northeast Parallel Architectures Center
at Syracuse University,
gcf@npac.syr.edu
and 
or 
so eigenvectors of different eigenvalues are orthogonal.
and 
are distinct eigenvectors
of same degenerate eigenvalue 
, then we can
replace 
by 
where 
is
a linear combination of 
and 
, and 
.