if nv(M)*K always has only real and positive eigenvalues, I believe that means it is symmetric PSD. if that is true, you can use lambda_sum_smallest. If that is not true, it is not convex.
Is is the obligation of forum question askers to prove their problem is convex, not of forum question answerers to prove their problem is non-convex
if you want to really understand convex optimization, study and solve exercises in https://web.stanford.edu/~boyd/cvxbook/
Please read Why isn't CVX accepting my model? READ THIS FIRST! .