Cauchy Matrix

In mathematics, a Cauchy matrix, named after Augustin Louis Cauchy, is an m×n matrix with elements aij in the form

a_{ij}={\frac{1}{x_i-y_j}};\quad x_i-y_j\neq 0,\quad 1 \le i \le m,\quad 1 \le j \le n

where and are elements of a field, and and are injective sequences (they do not contain repeated elements; elements are distinct).

The Hilbert matrix is a special case of the Cauchy matrix, where

Every submatrix of a Cauchy matrix is itself a Cauchy matrix.

Read more about Cauchy Matrix:  Cauchy Determinants, Generalization

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