Stability problems invariably impose constraints on eigenvalues and the spectral radius, Spr

, of a matrix

emerges as an important concept. Unfortunately, the spectral radius of a matrix does not qualify as a norm. Nevertheless, with the aid of the Lyapunov lemma we prove the following: let

denote a rational matrix in the

independent variables

, which is analytic in the closed unit polydisc,

. Let

denote the distinguished boundary of

. Then, Spr

for all

if and only if Spr

for all

. In addition to pointing out several obvious generalizations, we also employ the above theorem to give a rigorous proof of the long accepted conjecture that the absolute stability of a

-port amplifier can always be tested by closing its

-ports on

uncoupled pure reactances. Lastly, we present an entirely new justification of the well-known fact that a reciprocal

-port amplifier is absolutely stable if and only if it is strictly passive.