= Resolution of the identity
{title2=$\sum_j|j\rangle\langle j|=I$}
= Completeness relation
{synonym}
A complete <orthonormal basis> in a <Hilbert space> resolves the identity as $\sum_j|j\rangle\langle j|=I$. In infinite <dimension> the partial sums converge strongly: their <action> on each fixed vector converges in norm. Generalized <position> and <momentum> eigenstates instead give distributional <integral> resolutions, such as $\int dx\,|x\rangle\langle x|=I$, with their normalization interpreted through the <Dirac delta function>.
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