Interesting Facts on Eigenstates
The eigenstates of a matrix
However if we put in two real off-diagonal elements
the eigenstates becomes
If we are talking about real matrix,
even though it is true that the eigenstates are
the eigenstates are not that simple if we add in off-diagonal elements that make sure the matrix is still Hermitian.
In fact the eigenstates for the eigenequation
is given by
where $b^2 = b \cdot b$ is not the modulus squared.