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

Optimization of Real, Hermitian Quadratic Forms: Real, Complex Hopfield-Amari Neural Network