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”

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