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is [[compact operator|compact]] if it can be written in the form{{Citation needed|date=September 2011}}
<math display="block">\mathcal{L} = \sum_{n=1}^N \rho_n \langle f_n, \cdot \rangle g_n,</math>
where <math>1 \leq N \leq \infty,</math> and <math>\{f_1, \ldots, f_N\}</math> and <math>\{g_1, \ldots, g_N\}</math> are (not necessarily complete) orthonormal sets. Here <math>\rho_1, \ldots, \rho_N</math> are a set of real numbers, the [[singular value]]s of the operator, obeying <math>\rho_n \to 0</math> if <math>N = \infty.</math>
The bracket <math>\langle\cdot, \cdot\rangle</math> is the scalar product on the Hilbert space; the sum on the right hand side must converge in norm.
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