The Pseudoinverse - Numerical Linear Algebra

Описание: This discussion is all about the Moore-Penrose Pseudoinverse, or just Pseudoinverse for short. We explore the pesudoinverse numerically in python using numpy's linalg package.

Check out the code plus some additional written notes: https://github.com/nkphysics/Computat...

The Pseudoinverse leverages the Singular Value Decomposition (SVD) to work. If you need a refresher you can watch my discussion on the SVD here:    • Singular Value Decomposition (SVD) - Linea...  

For overdetermined systems the pseudoinverse helps in producing a least squares solution. If you need a refresher on the method of least squares check that out here:    • The Method of Least Squares - Linear Algebra  

My entire linear algebra playlist:    • Numerical Linear Algebra  


The following links will take you to the papers by E. H. Moore and Roger Penrose for the Pseudoinverse:

https://www.cambridge.org/core/journa...

https://www.ams.org/journals/bull/192...

This video has made use of the images credited to the following:

E.H. Moore: Unknown -- Historical photo, Public domain, via Wikimedia Commons

Roger Penrose: Cirone-Musi, Festival della Scienza, CC BY-SA 2.0 https://creativecommons.org/licenses/..., via Wikimedia Commons