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orthonormal basis ISIM

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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.
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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.
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