When we study mathematics, we encounter various number systems. Instead of going into rigorous definitions, let’s just briefly explore them. Natural Numbers Natural numbers (\(\mathbb{N}\)) are the numbers we use for counting and ordering. They start from 1 and go…
When Do We Use Functions? We use functions whenever one variable depends on another. For example, the cost per product (let’s call it \(y\)) usually varies depending on the quantity produced (denoted as \(x\)). In this scenario, we say that…
As a business professional, you rely on a wide range of mathematical tools, but none are arguably more frequently used than linear algebra and statistics. This is the first post in a series where we’ll explore how linear algebra provides…
When studying linear algebra, we are continuously faced with the word field. In most cases, we use the set of real numbers, which is an example of a field. But what is a field? A field is a set that…
What Is a Vector Space? Vector space? Sounds a little strange, right? But in fact, we use it almost every day. The numbers we work with daily form one example of a vector space, and when we run something like…
Matrix (and Matrices) are one of the most fundamental tools in mathematics, widely used in fields such as AI, physics, and economics. Let’s break down what a matrix is, how it’s structured, and some of the key terms you’ll often…
A subspace is a subset of a vector space that still behaves like a vector space under the same operations of addition and scalar multiplication (you can find the link to the Vector Space post at the bottom of this…
What is linear combinations? When we study linear algebra, we keep running into the idea of “linearity” in a few core ways. Each one focuses on a different kind of object: Today, we’ll start with linear combinations. What is a…
In our previous post, we explored Linear Combinations—the art of mixing vectors together to reach new points in space. It showed us what is possible to build. But in mathematics, as in business, just knowing what is possible isn’t enough;…
In linear algebra, we often want to find the simplest set of building blocks that can construct every single element in a space without any redundancy. This set is called a Basis. We are going to define a Basis using…