Advanced Linear Algebra - Lecture 35: Geometric Interpretation of the Singular Value Decomposition

We talk about how to think about the singular value decomposition geometrically. We introduce the idea that the singular values of a matrix are the radii of the ellipse (or ellipsoid, or hyperellipsoid) that the unit circle (or unit sphere, or unit hypersphere) is transformed into by that matrix.

Please leave a comment below if you have any questions, comments, or corrections.

Timestamps:
00:00 - Introduction
00:28 - Rotate, stretch, rotate
02:38 - 2D picture
04:21 - Circles and ellipses
06:06 - 3D picture

[dalisabe]

I would like to see the process in slow motion. Starting with some matrix, A, I would like to see the set of vectors that are rotated, stretched and then rotated again.