Basic symbols and terminology

First, let's take a look at the most basic symbols that are used in the mathematical process as well as some more subtle notations used by data scientists.

Vectors and matrices

A vector is defined as an object with both magnitude and direction. This definition, however, is a bit complicated for our use. For our purpose, a vector is simply a 1-dimensional array representing a series of numbers. Put in another way, a vector is a list of numbers.

It is generally represented using an arrow or bold font, as shown:

Vectors are broken into components, which are individual members of the vector. We use index notations to denote the element that we are referring to, as illustrated:

If then

Note

In math, we generally refer to the first element as index 1, as opposed to computer science, where we generally refer to the first element as index 0. It is important to remember what index system you are using.

In Python, we can represent arrays in many ways. We could...