  In distributed optimization or Nash-equilibrium seeking over directed graphs,
it is crucial to find a matrix norm under which the disagreement of individual
agents' states contracts. In existing results, the matrix norm is usually
defined by approximating the spectral radius of the matrix, which is possible
when the matrix is real and has zero row-sums. In this brief note, we show that
this technique can be applied to general square complex matrices. More
specifically, we prove that the spectral radius of any complex square matrix
can be approximated by its "weighted" spectral norm to an arbitrary degree of
accuracy.

Optimization and Control