In the first part of this book, we dig into the branch of math called linear algebra. At a very high level, linear algebra is the branch of math dealing with computations on multi-dimensional data. The concept of “dimension” is a geometric one; you probably intuitively know what I mean when I say “a square is 2-dimensional” while “a cube is 3-dimensional.” Among other things, linear algebra lets us turn geometric ideas about dimension into things we can compute concretely.
The most basic concept in linear algebra is that of a vector, which you can think of as a data point in some multi-dimensional space. For instance, you’ve probably heard of the 2-dimensional (2D) coordinate plane in high school geometry and algebra. As we’ll cover in chapter 2, vectors in 2D correspond to points in the plane, which can be labeled by ordered pairs of numbers of the form (x, y). In chapter 3, we’ll consider 3-dimensional (3D) space, whose vectors (points) can be labeled by triples of numbers in the form (x, y, z). In both cases, we see we can use collections of vectors to define geometric shapes, which can, in turn, be converted into interesting graphics.