  B. Afsari has recently proposed a new approach to the matrix joint
diagonalization, introduced by J.--F. Cardoso in 1994, in order to investigate
the independent component analysis and the blind signal processing in a wider
prospective. Delicate notions of linear algebra and differential geometry are
involved in the works of B. Afsari and the present paper continues such a line
of research, focusing on a theoretical condition which has significant
consequences in the numerical applications.
