# Introduction

Singular Value Decomposition (SVD) is based on a theorem from linear algebra that says a rectangular matrix $A$ can be represented as a product of three matrices:

- an orthogonal matrix $U$ (i.e., $UU^T = I$)
- a diagonal matrix $\Sigma$ and
- the transpose of an orthogonal matrix $V$ (i.e., $V^TV = I$)

**singular values**of $A$.

An eigenvector is a non-zero vector that satisfies the equation: $$A\vec{v} = \lambda\vec{v}$$ where $A$ is a square matrix, the scalar \lambda\ is called the eigenvalue.

# Computing SVD of a 2x2 matrix

You can use MATLAB or Octave or program using LAPACK directly to compute SVD but let's see how it's done. First, here's the Octave script