Eigenvalues of a Hermitian Matrix are Real saad0105050 Elementary, Expository, Mathematics, Matrix Analysis November 13, 2012March 17, 2018 1 Minute In this post, we prove the following: Statement: All eigenvalues of a Hermitian matrix are real. Proof: Since the matrix is Hermitian, by definition, Let be an eignevalue of , and be the corresponding eigenvector. Let and Then, The sum in the right hand side is real. It follows that will be real if and only if is real. Let us examine: Using , , thus must be real. Consequently, must be real. In another post, we have shown that for a Hermitian matrix, the eigenvectors pertaining to different eigenvalues are orthogonal. Advertisements Like this:Like Loading... Related Published by saad0105050 View all posts by saad0105050 Published November 13, 2012March 17, 2018

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