Author(s): Maxwell’s Demon

Originally published on Towards AI.

Demystifying the QR Decomposition

We are privileged. Today, we can build machine learning models almost effortlessly: import an open-source linear algebra or machine learning toolbox, write a few lines of code using appropriate subroutines (or outsource it to an LLM), and obtain a working solution. While this convenience is undeniably powerful, it comes at a cost, especially while learning. Relying on toolboxes does not create deep understanding.

This article explores the fundamental concepts of orthonormality and QR factorization, detailing the practical applications in linear algebra. It begins with the basics of linear algebra concepts, progresses through the Gram-Schmidt process for generating orthonormal bases, and elaborates on QR decomposition as a tool for solving linear systems and performing linear regression efficiently. The practical significance of these mathematical techniques is highlighted, emphasizing their utility in data science and engineering fields.

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Published via Towards AI