This video covers the QR decomposition in linear algebra, and 3 different methods of performing a QR decomposition.
We cover the following 3 methods of computing a QR decomposition:
- QR by the Gram-Schmidt Process
- QR by Householder transformations (reflections)
- QR by Givens Rotations
All 3 of these methods for computing a QR decomposition are demonstrated with python code.
All code, notes and references used in this discussion of the QR decomposition can be found here:
github.com/nkphysics/Computat...
If you need an in-depth look at the Gram-Schmidt process check out this previous video:
• The Gram-Schmidt Proce...
You can check out all my Linear Algebra videos here:
• Linear Algebra
Timestamps:
00:00 - Introduction
00:36 - QR decomposition overview
01:42 - Quick QR decomposition with numpy
02:24 - Overview of QR decomposition methods
02:57 - QR decomposition by the Gram-Schmidt process
07:26 - QR decomposition by Householder Transformations (reflections)
19:00 - QR decomposition by Givens Rotations
30:27 - Closing remarks and benefits of QR