Matrices - Introduction

Before you dive into matrices, make sure you’re comfortable with the concept of vectors.

The next important mathematical structure in the field of linear algebra is the matrix.

What Is a Matrix?

A matrix can be thought of in different ways. I will not give a definition which is too formal, since that would be beside the point, and the knowledge covered in the course would not suffice to understand it.

One way to think of a matrix is as a vector of vectors. Until now, I have only used numbers inside of vectors, but nothing stops us from putting a vector inside another vector. This idea is very common in computer science, since in low-level languages, there’s no such thing as a “matrix”, it’s really just an array of arrays.

Another way to think of a matrix is as a natural extension of a vector. What I mean is that a vector is basically an $n \times 1$ “grid”, and a matrix is a $m \times n$ “grid”.

Whatever model you like best, in essence, a matrix is just a rectangular arrangement of elements.