Matrix Madness

Linear algebra is an important tool used in modern deep learning algorithms. Unfortunately, when I did my undergrad in Electrical and Computer Engineering, I had no idea that the ability to transform vectors and matrices would ever be practicably useful for anything (other than giving me migraines at 2AM the night before my midterm exams). So, once I had learned enough to pass the course, I immediately forgot everything.

It was only when I decided to pursue a deeper understanding of machine learning and AI, in order to apply it to my business and to my work in finance, that it dawned on me. I should have paid attention in Linear Algebra II when I was back at the UofA in Engineering school! Well, since I didn’t, and even if I did, all my books on the subject mysteriously burned up in the great notes fire of ’09, I guess it’s time to re-learn me some matrix math.

Lucky for me, Udacity has brought on some of the best professional educators in the world for their AI Nanodegree program including former Khan Academy animator and 3 Blue 1 Brown creator, Grant Sanderson.

So, now I’m super good at manipulating matrices thanks to the magic of a YouTube superstar and the LaTeX plugin for WordPress websites.

A = \begin{bmatrix} a_{11} & \cdots & a_{1j} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots & \ddots & \vdots \\ a_{i1} & \cdots & a_{ij} & \cdots & a_{in} \\ \vdots & \ddots & \vdots & \ddots & \vdots \\ a_{m1} & \cdots & a_{mj} & \cdots & a_{mn} \end{bmatrix}

…I spent 30 minutes trying to get this matrix to display correctly.

If you want to learn why vectors are cool and how to use matrix multiplication to rule the world, watch the video series that I’ve linked below.

We haven’t arrived at the part about why Linear Algebra is so important for creating neural networks and deep learning algorithms, but we will. If you’re still with me, keep plugging along, learn how to understand all matrix transformations using only the unit vector and a 2×2 matrix. Eventually, we’ll discover how to program a computer to predict Apple’s  share price the day after they launch a ‘new’ iPhone

/insert corny iPhone XS Max joke here/.

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That’s all for today. Now go out on your own and learn the basics of linear algebra! If you message me directly, I’ll even send you my notes. Tomorrow, we’ll talk about why this stuff is important for machine learning.

Linear algebra joke: One year for halloween I was ‘Snakes on a Plane’

If you’re still here and you’re wondering why yesterday we were talking about valuing a company and today we’re talking about undergraduate linear algebra, you’re probably not alone. So I’ll tell you why: It’s going to take a foundational understanding of programming, mathematics and finance to get where we need to go. To understand machine learning, we have to understand how the software is built and to build software that is capable of doing what a CFA can do, we’ll need to know what a CFA knows. I’m bringing you along on this journey as I learn the fundamentals on both ends, machine learning and finance. Let’s see how it goes!

Do you get it now?