W3_L2: Orthogonal vectors & subspaces

Описание: Welcome to Week 3 Lecture 2 of the course "Machine Learning Foundations" by Profs. Harish Guruprasad Ramaswamy, Arun Rajkumar, and Prashanth LA.
Full Course: https://study.iitm.ac.in/ds/course_pa...

Video Overview
This lecture explores the fundamental concepts of orthogonality and orthogonal subspaces, which are central to projections and least squares methods. We begin by defining orthogonal vectors, understanding vector length, and exploring the inner product and dot product.We then extend the idea to orthogonal subspaces, discussing what it means for two subspaces to be orthogonal. Finally, we revisit the four fundamental subspaces of a matrix—column space, null space, row space, and left null space—and identify which pairs are orthogonal to each other. This understanding sets the stage for analyzing least squares problems in upcoming lectures.

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