Finding eigen value

Let us say L is a positive semi definite matrix ,how can i caleculate smallest non trivial eigen value of L in cvx?
1st eigen value of L is always zero so i used lambda_sum_smallest(L,2) which gives second smallest eigen value but some times multiplicity of 0 eigen value is more than one ,so please help me how to find smallest non trivial eigen value of L.

I’m afraid that’s not convex, unless the eigenspace of the zero eigenvalues is fixed.

Why not use eig function of MATLAB to calculate all of eigenvalues, then select the smallest non-trivial one? alternatively, you can try to utilize the Courant minimax principle, see
and Min-max theorem, see