Appendix C. Mathematical refresher
Throughout this book, we assumed little about the mathematical background of our audience. This appendix presents some of the mathematical formulas that we used in our algorithms, but never wrote explicitly in their standard form. The classic book that combines a solid mathematical description together with numerical algorithms is Numerical Recipes: The Art of Scientific Computing by William H. Pres et al. That book is a must-have reference for a large number of topics related to the development of intelligent algorithms.
In the context of elementary mathematics and physics, a vector is the mathematical representation of an arrow. The most common and intuitive example is an arrow that connects two points, say A and B on a plane. In the formulas that we used, a vector is represented by a one-dimensional array. In other words, it’s an ordered set of numbers. We typically denote vectors with a bold Latin letter, such as x. A 10-dimensional vector would be an ordered set of numbers xi, where the index i takes values between 1 and 10 (inclusive)—or 0 and 9 (inclusive), if you start counting from 0.