During my first year in graduate school, I had an epiphany about mathematics that changed my whole perspective about the field. I had chosen to study machine learning, a cross-disciplinary research area that combines elements of computer science, statistics, and numerous subfields of mathematics, such as optimization and linear algebra. It was a lot to take in, and all of us first-year students were struggling to absorb the deluge of new concepts.
One night, I was sitting in the office trying to grok linear algebra. A wonderfully lucid textbook served as my guide: Introduction to Linear Algebra, written by Gilbert Strang. But I just wasn’t getting it. I was looking at various definitions — eigen decomposition, Jordan canonical forms, matrix inversions, etc. — and I thought, “Why?” Why does everything look so weird? Why is the inverse defined this way? Come to think of it, why are any of the matrix operations defined the way they are?