  In this document I recapitulate some results by Hiriart-Urruty and Ye (1995)
concerning the properties of differentiability and the existence of lateral
directional derivatives of the multiple eigenvalues of a complex Hermitian
matrix function of several real variables, where the eigenvalues are supposed
in a decreasing order. Another version of these results was obtained by
Ji-guang Sun (1988).
  This 2020 version has been written following a remark raised by Miloud
Sadkane about the presence or not of the value 1/2 in the formulas that give
the lateral directional derivatives of multiple singular values. Therefore, I
have added Theorem 9. I have also written in more detail the relationship of
the reviewed results with those in the bibliography. Finally, I have also put a
result of mine (Corollary 11 in [1]) (joint with Armentia and Velasco) which
interprets a Lippert's Theorem (2005).
