# Eigendecomposition An **eigendecomposition** is simply a change of basis, where in this new basis a matrix $A$ is described via a *diagonal matrix* $\Lambda$: $\Lambda = U^{-1} A U $ And we can thus represent $A$ as: $A = U \Lambda U^{-1} $ **TODO: Visualize change of basis in notes or something** --- Date: 20220312 Links to: Tags: References: * [Eigendecomposition : Data Science Basics - YouTube](https://www.youtube.com/watch?v=KTKAp9Q3yWg&t=436s) * [Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra - YouTube](https://youtu.be/PFDu9oVAE-g?t=893) * [Eigenvalues and Eigenvectors. Explained by change of basis and… | by Risto Hinno | The Startup | Medium](https://medium.com/swlh/eigenvalues-and-eigenvectors-5fbc8b037eed)