of the data onto the unit sphere, have been proposed in [@LMSTZC1999] (see also [@Ger08] and [@TKO2012]).

We consider in this work another robust way of measuring association between variables, that can be extended directly to functional data. It is based on the notion of median covariation matrix (MCM) which is defined as the minimizer of an expected loss criterion based on the Hilbert-Schmidt norm (see [@KrausPanaretos2012] for a first definition in a more general $M$-estimation setting). It can be seen as a geometric median (see [@Kem87] or [@MNO2010]) in the particular Hilbert spaces of square matrices (or operators for functional data) equipped with the Frobenius (or Hilbert-Schmidt) norm. The MCM is non negative and unique under weak conditions. As shown in [@KrausPanaretos2012] it also has the same eigenspace as the usual covariance matrix when the distribution of the data is symmetric and the second order moment is finite. Being a spatial median in a particular Hilbert space of matrices, the MCM is also a robust indicator of central location, among the covariance matrices, which has a 50 % breakdown point (see [@Kem87] or [@MR2238141]) as well as a bounded gross sensitivity error (see [@CCZ11]).

The aim of this work 