Source Guide: Eigenvalues and Diagonalization

A curated source guide for learning eigenvalues and diagonalization from first pass through graph- and dynamics-facing research bridges.

Keywords

source guide, eigenvalues, diagonalization, spectral methods

1 How To Use This Guide

Use one layer at a time:

• First pass for the geometric and modal picture
• Second pass for more proofs and exercises
• Paper bridge for graph and spectral-learning directions

2 Stable Core

• MIT 18.06: Lecture 21, Eigenvalues and Eigenvectors - First pass - best official first stop for spectral intuition and computation. Checked 2026-04-24.
• MIT 18.06SC: Lecture 22, Diagonalization and Powers of A - First pass - official source for matrix powers and diagonalization. Checked 2026-04-24.
• Hefferon, Linear Algebra - Second pass - stronger self-study source for proof and exercise depth. Checked 2026-04-24.

3 Current Bridge

• A Comprehensive Survey on Spectral Clustering with Graph Structure Learning - Second pass - current map from classical spectral modes to graph clustering with learned structure. Checked 2026-04-24.

4 Paper Bridge

• Piecewise Constant Spectral Graph Neural Network - Paper bridge - current example of explicit spectral design in graph learning. Checked 2026-04-24.

5 Recommended Reading Paths

5.1 Path 1: First serious understanding

1. MIT 18.06 Lecture 21
2. MIT 18.06SC Lecture 22
3. Eigenvalues and Diagonalization

5.2 Path 2: Modes and dynamics

1. Eigenvalues and Diagonalization
2. Spectral Modes in Consensus and Graphs
3. Computation Lab: Matrix Powers and Spectral Modes

5.3 Path 3: Bridge to graph learning

1. Eigenvalues and Diagonalization
2. Spectral Clustering and Graph Modes
3. Spectral Methods from Graphs to GNNs

6 Sources Checked Online

All links above were checked on 2026-04-24.

The verification pass included:

• official MIT OCW pages
• official author-maintained textbook page
• current arXiv survey page for spectral clustering
• current OpenReview page for a spectral GNN paper