In this brain-friendly deep dive, we’re stripping Principle Component Analysis down to its first principles. You won’t just learn how to use it; you’ll master the underlying logic and the math that makes it work—no hand-waving or vague metaphors required. By pairing theory with practical code, we’ll move beyond simply calling libraries to achieving a true, foundational understanding of the ‘why’ behind the ‘how.
The Singular Value Decomposition (SVD) is “a highlight of linear algebra” to quote Prof. Strang ( [1] p. 371). However, I must confess that when I studied it I had a difficult time understanding it and this was due to how it was presented. The SVD is often introduced as a given formula which is then shown to just work. But it always felt very unsatisfying to me not knowing why. So – here is the SVD explained the way I wish I had been taught, which is deriving it from first principles.
Why do orthogonal matrices rotate while diagonal matrices stretch?
In this deep dive into linear algebra, we prove the geometric intuition behind the Singular Value Decomposition (SVD). By examining how inner products are preserved and how basis vectors are scaled, I demonstrate why linear transformations are restricted to these specific movements.
Master Spectral Decomposition. Learn how symmetric matrices are diagonalized into orthogonal eigenvectors and eigenvalues with clear geometric intuition.
Your Friendly Guide to the Math behind Data Science and AI 1 Introduction Matrix diagonalization is a crucial concept in linear algebra with tons of applications. Even more importantly, it is
The complete, friendly deep-dive into the core linear algebra every Data Scientist needs. 1 Introduction Have you ever wondered how to unlock the secrets hidden in data but felt overwhelmed
