Un d\'eterminant reproduisant

TL;DR

This paper evaluates a specific determinant involving six variables and shows that its form reproduces the structure of its entries, providing insight into its algebraic properties.

Contribution

The paper derives a formula for the determinant as a function of the last sextuplet, revealing a reproducing structure similar to the original matrix entries.

Findings

The determinant can be expressed in a form that reproduces its entries.

The structure of the determinant is preserved under certain transformations.

Provides a new perspective on the algebraic properties of this class of determinants.

Abstract

We evaluate the determinant D = det((y_j u_i - x_j v_i)/(l_j - k_i)) as a function of the last sextuple (u,v,k;x,y,l), the result being shown to have a form reproducing the one of the entries of D. ----- Nous calculons le d\'eterminant D = det((y_j u_i - x_j v_i)/(l_j - k_i)) comme fonction du dernier des sextuplets (u,v,k;x,y,l), en exprimant le r\'esultat sous une forme qui reproduit celle des entr\'ees de D.