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orthonormal basis MAT.

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The only possible measurement is between any two orthogonal states (an orthonormal basis). en.wikipedia.org

Any separable inner product space has an orthonormal basis. en.wikipedia.org

If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis. en.wikipedia.org

Physicists commonly regard a density operator as being represented by a (possibly infinite) density matrix relative to some orthonormal basis. en.wikipedia.org

The result does not depend on the choice of orthonormal basis. en.wikipedia.org

Within this orthonormal basis, the structure constants are then antisymmetric with respect to all three indices. en.wikipedia.org

For example, it is often desirable to compute an orthonormal basis for a space, or an orthogonal change of bases; both take the form of orthogonal matrices. en.wikipedia.org

Every symmetric matrix is thus, up to choice of an orthonormal basis, a diagonal matrix. en.wikipedia.org

A particular case is obtained when these vectors form an orthonormal basis, that is, they are all perpendicular to each other. en.wikipedia.org

The eigenstates have a physical meaning further than an orthonormal basis. en.wikipedia.org

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