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What is an eigendecomposition? In this video, we explore how symmetric matrices can be written as a rotation, a stretching along principal axes, and a rotation back. This factorisation is built entirely from eigenvalues and eigenvectors, and is known as the eigendecomposition. Understanding this structure is a key step towards more advanced ideas such as the Singular Value Decomposition (SVD). Check out my full Linear Algebra Basics playlist here: https://www.youtube.com/playlist?list=PLlenrM60CLlM1C6JDdtVBz1LOzIwTSNCm 📌 Timestamps: 0:00 Introduction 0:56 Recap: Eigenvectors 1:36 Symmetric Matrices and Enough Eigenvectors 4:27 From Eigenvectors to Eigendecomposition 10:37 Geometric Interpretation 11:32 Example: A Symmetric 2×2 Matrix 14:26 Matrix Powers Made Simple
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