# Eigendecomposition

## Table of Contents

## 1 Introduction

Let \( A \) be an \( n \times n \) matrix with \( n \) **linearly independent** eigenvectors \( v_1 ... v_n \), then we can write \( A \) as:

\[ A = PDP^{-1} \]

Where \( P \) is the matrix whose ith column is \( v_i \) and \( D \) is a diagonal matrix with \( D_{i,i} = \lambda_i \).

**Proof**: