A simple proof of a necessary and sufficient condition for absolute stability of symmetric neural networks

The main result that for a neural circuit of the Hopfield type with a symmetric connection matrix T, the negative semidefiniteness of T is a necessary and sufficient condition for absolute stability was obtained and proved by rather complex procedures by Forti et al. [1994]. This brief gives a very simple proof of this result, using only the well-known total stability result about Hopfield type neural circuits with a symmetric connection matrix and the basic algebraic properties of real symmetric matrices