  In this research paper, the problem of optimization of quadratic forms
associated with the dynamics of Hopfield-Amari neural network is considered. An
elegant (and short) proof of the states at which local/global minima of
quadratic form are attained is provided. A theorem associated with local/global
minimization of quadratic energy function using the Hopfield-Amari neural
network is discussed. The results are generalized to a "Complex Hopfield neural
network" dynamics over the complex hypercube (using a "complex signum
function"). It is also reasoned through two theorems that there is no loss of
generality in assuming the threshold vector to be a zero vector in the case of
real as well as a "Complex Hopfield neural network". Some structured quadratic
forms like Toeplitz form and Complex Toeplitz form are discussed.
