# SVD

## What is it?

mxn matrix *A* = *U*Σ*V*^{T}, where ...

## What does it mean?

Any matrix just does rotate-scale-rotate

(Strictly speaking can combine axis flips with rotation.)

## What does it look like?

Some examples of SVD, showing shapes of A, U, Σ, *V*^{T}:

A in blue, U in yellow, sigma in red, VT in green

## How to calculate it?

Look at *A*^{T}*A* and *A**A*^{T}

## What is it good for?

### 1. low-rank approximation of matrices

Approximation of matrix by sum of rank-1 matrices (data compression)

Examples

i.
O'Brian 112

ii.
student gallery

### More applications on Thursday