This is an elementary (yet important) fact in matrix analysis.
Statement
Let be an complex Hermitian matrix which means where denotes the conjugate transpose operation. Let be two different eigenvalues of . Let be the two eigenvectors of corresponding to the two eigenvalues and , respectively.
Then the following is true:
Here denotes the usual inner product of two vectors .
Continue reading “In a Hermitian Matrix, the Eigenvectors of Different Eigenvalues are Orthogonal”