Cauchy matrix
In mathematics, a Cauchy matrix, named after Augustin-Louis Cauchy, is an m×n matrix with elements aij in the form a i j = 1 x i − y j ; x i − y j ≠ 0 , 1 ≤ i ≤ m , 1 ≤ j ≤ n {\displaystyle a_{ij}={\frac {1}{x_{i}-y_{j}}};\quad x_{i}-y_{j}\neq 0,\quad 1\leq i\leq m,\quad 1\leq j\leq n} where x i {\displaystyle x_{i}} and y j {\displaystyle y_{j}} are elements of a field F {\displaystyle {\mathcal {F}}} , and ( x i ) {\displaystyle (x_{i})} and ( y j ) {\displaystyle (y_{j})} are injective sequences (they contain distinct elements). == Properties == Every submatrix of a Cauchy matrix is itself a Cauchy matrix.