#### Overview of this book

In this book, you'll embark on a comprehensive journey through the fundamentals of linear algebra, a critical component for any aspiring machine learning expert. Starting with an introductory overview, the course explains why linear algebra is indispensable for machine learning, setting the stage for deeper exploration. You'll then dive into the concepts of vectors and matrices, understanding their definitions, properties, and practical applications in the field. As you progress, the course takes a closer look at matrix decomposition, breaking down complex matrices into simpler, more manageable forms. This section emphasizes the importance of decomposition techniques in simplifying computations and enhancing data analysis. The final chapter focuses on principal component analysis, a powerful technique for dimensionality reduction that is widely used in machine learning and data science. By the end of the course, you will have a solid grasp of how PCA can be applied to streamline data and improve model performance. This course is designed to provide technical professionals with a thorough understanding of linear algebra's role in machine learning. By the end, you'll be well-equipped with the knowledge and skills needed to apply linear algebra in practical machine learning scenarios.
Free Chapter
Chapter 1: We Start Here
Chapter 2: Why Linear Algebra?
Chapter 4: But What About a Matrix?
Chapter 5: Break Them Down - Matrix Decomposition
Chapter 6: The Final Stretch - Principal Component Analysis

# Chapter 1We Start Here

This book is a story about linear algebra, the main character of which is the star of this discipline, the vector. We will start by defining this concept, that prides itself on its simplicity. But don’t mistake simplicity for lack of power; from an uncomplicated vector we will arrive at complex methods like the single value decomposition and the principal component analysis.

My journey began when I was only four years old, and my father gave me my first book on equations. Since then, I have never looked back. Mathematics flowed in my mind, and calculations came out as naturally as a delicate butterfly landing on a ravishing red petal of this miracle of nature that we so often call a flower… don’t be scared already! We are just at the second paragraph, and this is not true. I am just a regular guy who was most likely kicking a ball around when he was four. But, being a typical fellow, my struggle with mathematics was real during a specific time in my life, my first couple of years at university. This was because of a combination of a bad attitude and a need for content to be structured more like a story than a manual. I was scared of equations and blamed everything I could, except myself, for my lack of success in understanding mathematics. When I look back now, I can see that it is impossible to understand anything with that attitude.

Symbols and Greek letters are the alphabets of mathematics, whereas equations are the words that represent abstract concepts. One needs to try to understand how to read this syntax, as it will bring significant benefits in the future. Unfortunately, mathematics has no sound, so I don’t think you can expect good results by using a hands-on approach where you learn by ignoring the syntax, as you might do with a musical instrument. Still, as a mathematician, I can’t say that this way is not possible. After all, the realm of uncertainty is where we do our best work. Once I overcame this first hurdle and I started to be able to read equations, another issue arose. I knew concepts in isolation, but relating them to one another seemed impossible. Different books have distinct structures and expose the same ideas in varying sequences, which became another obstacle for me. Now I say that I was lucky, but at the time, I considered myself the unluckiest person in the world. I could not have been more wrong.

The itinerary whereby I began putting concepts together and understanding mathematics started on the day I missed the meeting where we, the students, were due to meet the professors who would be supervising our university theses. I can’t provide a good reason for missing this meeting that won’t make you think I am an idiot, but hey, sometimes things have a funny way of resolving themselves.