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
