Mathematical Preliminaries

Abstract

In this book we shall be dealing with neural networks, artificial and biological. In an attempt to approach them and also higher-level mental processes scientifically, we cannot avoid setting up analytical (mathematical) system models. Many cognitive effects cannot be interpreted at all until one understands the nature of collective interactions between elements in a complex system. When dealing with spatially and temporally related samples of signal values that represent “information,” we thus need a mathematical framework for the description of their quantitative interrelations. This framework is often provided by the generalized vector formalism. The operations in vector spaces, on the other hand, can conveniently be manipulated by matrix algebra. These concepts are first introduced in Sect. 1.1.