Normal Operators

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Normal operators. Characterization of normal operators by ||Tv|| = ||T*v|| for all v. Eigenvectors of a normal operator corresponding to distinct eigenvalues are orthogonal.
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About the last result: can anything be said about eigenvectors corresponding to multiplicities of eigenvalues? Are they also orthogonal?

garfieldnate
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This kind of explanation feels like robotic

Pp-plhh