Five Factorizations of a Matrix

A Vision of Linear Algebra
Instructor: Gilbert Strang
View the complete course: https://ocw.mit.edu/2020-vision
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61iQEFiWLE21EJCxwmWvvek

Uploaded 06-12-23

In this video, Professor Strang provides an overall look at linear algebra by highlighting five different ways that a matrix gets factored.

For every matrix A, four key vector spaces are the row space and nullspace of A and its transpose.
To compute with A, we factor it into A = (column space basis) times (row space basis).
The simplest basis uses independent columns taken directly from the matrix A.
The best bases of all use *orthogonal* vectors from the column space and the row space of A.
These “singular vectors” produce the great Singular Value Decomposition!

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