Elegant SciPy

Chapter 6. Linear Algebra in SciPy

No one can be told what the matrix is. You have to see it for yourself.

Morpheus, The Matrix

Just like Chapter 4, which dealt with the FFT, this chapter will feature an elegant method. We want to highlight the packages available in SciPy to do linear algebra, which forms the basis of much scientific computing.

Linear Algebra Basics

A chapter in a programming book is not really the right place to learn about linear algebra itself, so we assume familiarity with linear algebra concepts. At minimum, you should know that linear algebra involves vectors (ordered collections of numbers) and transforming them by multiplying them with matrices (collections of vectors). If all of this sounds like gibberish to you, you should probably pick up an introductory linear algebra textbook before reading this. We highly recommend Gil Strang’s Linear Algebra and Its Applications (Pearson, 1994). An introduction is all you need, though—we hope to convey the power of linear algebra while keeping the operations relatively simple!

As an aside, we will break Python notation convention in order to match linear algebra conventions. In Python, variable names should usually begin with a lowercase letter. However, in linear algebra, matrices are denoted by a capital letter, while vectors and scalar values are lowercase. Since we’re going to be dealing with quite a few matrices and vectors, following the linear algebra convention helps to keep them straight. Therefore, ...