| 21. | Orthonormal is nice in general but not necessary here.
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| 22. | Popular tetrad bases include orthonormal tetrads and null tetrads.
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| 23. | If the basis vectors are orthonormal, then this is the unit pseudoscalar.
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| 24. | This is equivalent to the assertion that every Hilbert space has an orthonormal basis.
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| 25. | A basis for consisting of mutually orthogonal unit vectors is called an orthonormal basis.
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| 26. | Variations on the above example include the orthonormal frame bundle of a Riemannian manifold.
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| 27. | However, orthonormal bases are easier to manipulate and are often used in practice.
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| 28. | By the spectral theorem, there is a complete orthonormal set of eigenfunctions in with
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| 29. | In fact let be an orthonormal basis of and let be an element in.
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| 30. | :: No, they're not orthonormal; they are parallel though.
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