Applied General Systems Research pp 563-573 | Cite as

# A Matrix Algebra for Neural Nets

Chapter

## Abstract

Almost thirty-five years ago in their classic paper, McCulloch and Pitts (1943) described a method for modeling the nervous system. The basic idea of McCulloch and Pitts’ paper is that the nervous system can be described as a finite set of elements, called neurons, that have only two states, “on” and “off,” They assumed that time could be quantized into a set of discrete instants, so that the state of a neuron at the next instant of time would be a function of the present states of the neurons (and external inputs) that impinged on it.

## Keywords

Fast Fourier Transform Finite Field Matrix Algebra Convolution Theorem Field Linearization## Preview

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## References

- 1.E.R. Caianiello, “Some remarks on the temorial linearization of general and linearly separable Boolean functions.” Kybernetik 12, 1973, pp. 90–93.CrossRefGoogle Scholar
- 2.P. Call, “Linear analysis of switching nets,” Kybernetik 8, 1971, pp. 31–39.CrossRefGoogle Scholar
- 3.J.L.S. da Fonseca and W.S. McCulloch, “Synthesis and linearization of nonlinear feedback shift registers.” MIT Research Laboratory of Electronics Quarterly Progress Report No, 86, 1967, pp. 355–366.Google Scholar
- 4.H.D. Landahl and R Runge, “Outline of a matrix calculus for neural nets.” Bull. Math. Biophys. 8, 1946, pp. 75–81,CrossRefGoogle Scholar
- 5.W.S. McCulloch and W.H. Pitts, “A logical calculus of the ideas immanent in nervous activity.” Bull. Math. Biophys. 5, 1943, pp. 115–133.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 1978