I would like to compute the entropy of a positive definite matrix M, as defined by the entropy of the vector formed by the (positive) eigenvalues of M.

The corresponding matlab command is pretty simple, namely sum( entr( eig( M ) ) ).
However, I do not manage to adapt this expression to fit the CVX framework.

Thanks for your comment mcg.
It is quite unfortunate, since this type of spectral functions (provably convex or concave depending on the sign put in front of the entropy) is definitely of interest in many problems.
Let us wait some other responses

We actually discussed matrix entropy at some point. The problem is that CVX’s solvers require problems to be representable as SDPs. To our knowledge there is no way to represent matrix entropy using SDP. I am reasonably sure that cannot be done, at least not exactly.