RES.18-010 | Spring 2020 | Undergraduate

A Vision of Linear Algebra

2023 Video

Description

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!

Slides Used in this Video: Five Factorizations of a Matrix (PDF)

Instructor: Gilbert Strang

Course Info

Departments
As Taught In
Spring 2020
Learning Resource Types
Lecture Videos
Online Textbook