 Cauchy matrix (source code)

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= Cauchy matrix
{c}
{title2=$C_{ij}=1/(x_i+y_j)$}

A <Cauchy matrix> has entries $1/(x_i+y_j)$ with nonzero denominators. If $x_i=y_i>0$ are distinct, it is positive definite: $C_{ij}=\int_0^\infty e^{-x_is}e^{-x_js}ds$ is the Gram matrix of linearly independent exponential functions. This form occurs in finite-rank <inverse scattering transform> reconstructions.

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