Linear algebra

In this section, we introduce notation to describe vectors and matrices, which are key mathematical objects that we will encounter again and again throughout this book.

Vectors

In many circumstances, we will want to represent a set of numbers together. For example, the numbers 7.3 and 1.2 might represent the values of two features that correspond to a data point in a training set. We often group these numbers together in brackets and write them as (7.3, 1.2) or [7.3, 1.2]. Because of the similarity to the way we write spatial coordinates, we tend to call a collection of numbers that are held together a vector. A vector can be two-dimensional, as in the example just given, or d-dimensional, meaning it contains d components, and so might look like .

We can write a vector in two ways. We can write it as a row vector, going across the page, such as the following vector:

d-dimensional row vector

Eq. 8

Alternatively, we can write it as a column vector going...