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Diagonalisation of Hermitian Matrices

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The eigenvalues $ \lambda_i$ of a hermitian matrix $ A \; (A=A^*)$ are real, and there exists an ONB consisting of eigenvectors $ v_i$. Therefore

$\displaystyle U^*AU=$diag$\displaystyle (\lambda_1,\ldots,\lambda_n)\,, $

where $ U=(v_1,\ldots,v_n)$ is an unitary matrix.

The special case of real symmetric matrices $ (A=A^{\operatorname t})$ provides real eigenvalues.

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