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=====Lecture (10 minutes - 40 minutes with proofs)=====

  * Hermitian matrices have real eigenvalues.  
  * Hermitian matrices have one eigenvector for each eigenvalue (except for degeneracy).
  * The eigenvectors of a Hermitian matrix are orthogonal and can be normalized, //i.e.// they are orthonormal.
  * The eigenvectors of a Hermitian matrix form an orthonormal basis for the space of all vectors in the vector space.
  * Commuting operators share the same eigenbasis.

Notes for this lecture:
  * Use bra-ket notation for proofs.
  * Refer to specific examples from eigenvectors/eigenvalues activity.
  * (Optional) Refer to example of Fourier series.

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