Vectors

Introduction

There are many different definitions and interpretations of a vector, depending on the context and the field of study. Here we’ll briefly review two:

• A geometric interpretation, which is often used in physics and engineering

• An algebraic interpretation, which is often used in mathematics and computer science

In both cases, vectors are often represented as column matrices, i.e. as a collection of numbers, whose order is important, written top to bottom in a column. The two sections below give a brief overview of these two interpretations, and the operations that can be performed on vectors (such as addition, scalar multiplication, and the dot product).

Each section is followed by a set of exercises to test your understanding of the material. The answers to the exercises are provided after each section, so you can check your work. If the material is familiar to you, there is no need to complete every exercise.