How to use CVX minimize “trace(inv(X))”, where X is an N*N matrix

help trace_inv

trace_inv Trace of the inverse of a PSD matrix.

For square matrix X, trace_inv(X) is TRACE(INV(X)) if X is Hermitian

or symmetric and positive definite; and +Inf otherwise.`An error results if X is not a square matrix. Disciplined convex programming information: trace_inv is convex and nonmonotonic (at least with respect to elementwise comparison), so its argument must be affine.`

This is listed in http://cvxr.com/cvx/doc/funcref.html#new-functions . You should read the entire CVX Users’ Guide.