This paper considers theL2stability ofn-input/n-output linear, time-invariant feedback systems. It is demonstrated that the ring of all linear, bounded, time-invariant (LBTI) operators ofL2into itself is isomorphic with a commutative ringK(0) of bounded and holomorphic complex functions with domain the open right-half plane (ORHP). Necessary and sufficient conditions forn-input/n-output stability are derived from the conditions of invertibility of matrices over the ringK(0). Furthermore, a comprehensive analysis is given of the geometric interpretation of the stability conditions leading to a generalized Nyquist criterion. It is shown that the properties of a system matrixA∈K(0)n×nassociated with its invertibility inK(0)n×ncan be deduced from simple encirclement conditions in the complex plane involving the loci of the eigenvalues ofA.