Orthonormal basis
= Orthonormal basis
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= Orthonormal bases
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An orthonormal basis of a <Hilbert space> is an <orthonormal set> whose <linear span> has the whole space as its <closure>. This <completeness of an orthonormal system> allows every vector to be expanded in the basis vectors, with convergence in norm. In finite dimension it is also a <basis> in the finite-linear-combination sense.