| 11. | The following results are true for orthonormal bases, not orthogonal ones.
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| 12. | Every orthonormal basis in a separable Hilbert space is a Schauder basis.
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| 13. | For the last, you typically pick an orthonormal basis.
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| 14. | Thus an orthonormal basis can be chosen on each eigenspace so that:
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| 15. | In particular, every orthonormal set of vectors is isotropic.
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| 16. | The columns in are orthonormal and can be extended to an orthonormal basis.
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| 17. | The columns in are orthonormal and can be extended to an orthonormal basis.
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| 18. | These orbitals form an orthonormal basis for the wave function of the electron.
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| 19. | Here the frames are required to be orthonormal with respect to the metric.
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| 20. | Suppose that orthonormal eigenvectors of " T " have been found.
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