Five Factorizations of a Matrix

A Vision of Linear Algebra
Instructor: Gilbert Strang
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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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