What the hell is a matrix, anyways?
When I say matrix, you probably don’t have a great idea of what a matrix actually is, and that’s what I aim to solve.
What the hell is a vector, really?
This section draws heavily on the textbook Linear Algebra Done Right by Sheldon Axler
In the previous issue I didn’t go that deeply into the mathematical definition behind a vector. Sadly, before we can truly understand what a matrix is, we must first understand what a vector is.
In grade school, you should have learned about $\mathbb{Q}$, the rational numbers, $\mathbb{Z}$, the integers, and most importantly for this discussion, $\mathbb{R}$, the set of all real numbers. The set of the real numbers ($\mathbb{R}$) include the rational numbers and the irrational numbers. It does not include what we call imaginary numbers: numbers that include an imaginary part, $i$, the imaginary unit, which is defined as the $\sqrt{-1}$. A complex number is an ordered pair $(a, b)$, where $a, b \in \mathbb{R}$, and written as $a + bi$. We denote the set of all complex numbers with $\mathbb{C}$. We define $\mathbb{F}$ as either $\mathbb{R}$ or $\mathbb{C}$.
Note: This post is a work in progress — full matrix implementation coming soon.