Reduced dimension and multiple eigenvalues of a 4 x 4 diagonalizable matrix

a(xi) is a 4 x 4 matrix, of real linear forms on a real vector space of fin ite dimension. We state that, if the reduced dimention of a is superior or egal to 8 and a is diagonalizable with respect to a vector N, the character istic set: det a(xi) = 0, has, at less, a triple point different from 0. (C ) 2000 Editions scientifiques et medicales Elsevier SAS.