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== Most common usage ==
A ''positive semi-definite function'' of a [[real number|real]] variable ''x'' is a [[complex number|complex]]-valued function <math> f: \mathbb{R} \to \mathbb{C} </math> such that for any real numbers ''x''<sub>1</sub>, …, ''x''<sub>''n''</sub> the ''n'' × ''n'' [[matrix (mathematics)|matrix]]
:<math> A = \left(a_{ij}\right)_{i,j=1}^n~, \quad a_{ij} = f(x_i - x_j) </math>
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