# Singular Value Decomposition

Singular Value Decomposition

The singular value decomposition is a factorization of a matrix into . A vector is first rotated by an angle β via x, then x is scaled by a diagonal matrix to form . Finally the vector is rotated by an angle ω to form .

A

A=UΣ

T

V

x

T

V

T

V

Σ

Σx

T

V

Σx

T

V

b=UΣx=Ax

T

V