Cauchy matrix

Let x1, x2,,xm, and y1, y2,yn be elements in a field F, satisfying the that

  1. 1.

    x1,,xm are distinct,

  2. 2.

    y1,,yn are distinct, and

  3. 3.

    xi+yj0 for 1im, 1jn.

The matrix


is called a Cauchy matrix over F.

The determinantMathworldPlanetmath of a square Cauchy matrix is


Since xi’s are distinct and yj’s are distinct by definition, a square Cauchy matrix is non-singular. Any submatrixMathworldPlanetmath of a rectangular Cauchy matrix has full rank.

Title Cauchy matrix
Canonical name CauchyMatrix
Date of creation 2013-03-22 14:30:43
Last modified on 2013-03-22 14:30:43
Owner kshum (5987)
Last modified by kshum (5987)
Numerical id 9
Author kshum (5987)
Entry type Definition
Classification msc 15A57
Defines Cauchy matrices