Chapter Summary

    Matrix mathematics is very important to neural networks. Java does not include built-in support for matrixes; thus, three matrix classes have been presented here. These matrix classes are used to both create matrixes and perform various mathematical operations on them.

    Bipolar notation is a special way of representing binary values. In bipolar notation, the binary value of true is represented with a one, and the binary value of false is represented with a negative one. Most neural networks that work with binary values will make use of bipolar notation. The Hopfield neural network, which will be introduced in chapter 3, makes use of bipolar numbers.

    This book will make use of the matrix classes presented in this chapter for all neural networks that will be introduced. This will allow you to quickly see the mathematical underpinnings of each neural network.