The Ultimate Resource Library — Books, Lectures, Videos, Papers & More
The gold standard textbook for linear algebra. Strang's intuitive, geometric approach makes eigenvalues come alive. Chapters 6 covers eigenvalues, diagonalization, and differential equations. Widely used at MIT and hundreds of universities worldwide. Companion video lectures are free on MIT OCW.
One of the most widely adopted linear algebra textbooks in the world. Excellent for building computational intuition with eigenvalues and eigenvectors. Chapter 5 is dedicated entirely to eigenvalues with many real-world applications. Extremely clear writing.
A beautifully written, proof-focused textbook that takes a "determinant-free" approach to eigenvalues — introducing them through the concept of invariant subspaces. The 4th edition is legally free as Open Access. Chapters 5 (Eigenvalues & Eigenvectors) and 7 (Operators on Inner Product Spaces / Spectral Theorem) are masterful.
Comprehensive treatment connecting theory to applications. Deep coverage of eigenvalue perturbation theory, Gerschgorin circles, and the power method. Excellent for engineers and applied mathematicians.
The "bible" of numerical linear algebra. Covers QR algorithm, Lanczos method, Jacobi iteration, and every numerical method for computing eigenvalues. Essential for anyone implementing eigenvalue algorithms in production code.
Focused specifically on linear algebra for data scientists. Covers eigendecomposition, PCA, SVD, and dimensionality reduction with Python code. Chapters 13–15 are devoted to eigenvalues, SVD, and applications. Uses NumPy throughout.
Two-part structure: Part I covers theory (vector spaces, eigenvalues), Part II has 500+ solved problems with engineering and real-world applications. Great for practice and exam preparation.
A rigorous, proof-based textbook used in many advanced undergraduate courses. Chapter 5 on eigenvalues includes diagonalization, invariant subspaces, and the Cayley-Hamilton Theorem. Excellent for math majors.
A concise, elegant treatment by a master mathematician. Covers eigenvalues, spectral theorem, Jordan canonical form. Best for students with some mathematical maturity.
By Stanford professors. Focuses on applications: least squares, data fitting, and optimization. While it doesn't focus heavily on eigenvalues directly, it provides essential context for how linear algebra is applied in data science and control. The PDF is legally free.
Full textbook legally free under Open Access from Springer. One of the most elegant linear algebra books ever written.
A complete, free linear algebra textbook covering eigenvalues, eigenvectors, diagonalization, and Jordan form. Comes with a full solutions manual, also free. Covers 400+ exercises.
Originally published by McGraw-Hill, now available free as an open edition. Covers eigenvalues, diagonalization, and applications including Markov chains and dynamical systems. 650+ pages.
UC Davis lecture notes structured as a full textbook. Covers eigenvalues, eigenvectors, diagonalization, Jordan form. Clear, concise, and organized by lecture.
Free, open-source textbook. Chapter EE covers eigenvalues and eigenvectors. Available online and as PDF. Part of the Open Textbook Library.
Beautiful, interactive online textbook with embedded visualizations. Chapter 5 covers eigenvalues with interactive demos showing how eigenvectors behave under transformation.
Chapter 4 covers Matrix Decompositions (eigendecomposition, SVD). Chapter 10 covers PCA as a direct application. Bridges linear algebra and machine learning perfectly.
Curated open textbook with chapter 5 on eigenvalues. Exercises link directly to solutions. Clean formatting.
THE most famous linear algebra course in the world. Lecture 21 covers eigenvalues & eigenvectors, Lecture 22 covers diagonalization, Lectures 23–24 cover differential equations and Markov matrices. Strang's teaching is legendary.
The "Scholar" version includes additional recitation videos, problem sets with solutions, and study guides. Section 2.8 is the eigenvalue/eigenvector summary.
Strang's more advanced course focusing on SVD, PCA, deep learning connections, and eigenvalue applications in data science. A perfect follow-up to 18.06.
The complete Chapter 6.1 from Strang's "Introduction to Linear Algebra" textbook, made available as a free sample.
Concise review covering eigenvalues as optimization (Rayleigh quotient), matrix calculus, and applications in machine learning. Used as background material for Stanford's ML course.
Lecture on eigenvalues of Hermitian matrices, spectral theorem proof, and applications in spectral graph theory. From Stanford's algorithms course.
Notes from Stanford's Mathematical Methods for Robotics, Vision, and Graphics. Covers eigenvalues with applications in computer graphics and physics simulation.
Lecture notes from the famous Stephen Boyd (of convex optimization fame). Covers eigenvectors, diagonalization, and applications in linear dynamical systems.
Graduate-level numerical methods for eigenvalue computation. Covers QR algorithm, Krylov subspace methods, and large-scale eigenvalue problems.
Clear, self-contained lecture notes covering the definition, computation, and basic properties. Great for quick review.
Lecture slides covering Section 5.1 with worked examples and geometric interpretations. Useful for exam review.
Comprehensive notes bridging linear algebra with differential equations and control theory. Shows how eigenvalues connect to system stability.
Department of Mathematics lecture notes covering the fundamentals of linear algebra including eigenvalue decomposition.
Full-semester lecture notes with companion YouTube videos. Covers eigenvalues, diagonalization, and applications.
Canadian open math textbook covering linear algebra. Available as interactive HTML.
The most beautiful visual explanation of linear algebra ever created. Episode 14 covers eigenvectors and eigenvalues with stunning animations. Episode 15 shows a quick trick for computing eigenvalues of 2x2 matrices. Absolutely essential viewing.
🔗 Eigenvectors & Eigenvalues Lesson
The complete MIT linear algebra course. Strang is a legendary teacher. Lectures 21–25 cover eigenvalues, diagonalization, differential equations, symmetric matrices, and positive definite matrices.
Step-by-step video explanations with practice exercises. Perfect for absolute beginners who need patient, detailed explanations of every calculation step.
Called "the best online course on Linear Algebra" by many students. Covers eigenvalues, diagonalization, and spectral theory with clear visual explanations and great energy. Available freely on YouTube.
Extremely detailed, patient, and thorough explanations. Great for students who need every single step spelled out. Popular among community college and university students.
Axler himself teaches through his textbook, covering generalized eigenvectors, Jordan form, and the spectral theorem. Great companion to the free PDF textbook.
Videos paired with downloadable guided notes PDFs. Covers eigenvalues, eigenvectors, and their applications.
Focused specifically on the linear algebra needed for ML. Week 5 covers eigenvalues, eigenvectors, and their role in PCA. Taught by Imperial College faculty. Can audit for free.
Concise course covering matrix operations, eigenvalues, and applications to engineering problems. Can audit for free.
Rigorous course from UT Austin covering eigenvalues and their computation. Includes programming exercises in MATLAB/Octave.
Aggregator of 1600+ online linear algebra courses from universities worldwide. Filter by level, language, and platform.
Ch. 4: Matrix Decompositions (Eigendecomposition, SVD). Ch. 10: Dimensionality Reduction with PCA. The bridge between linear algebra and ML.
72-page reference of matrix identities, derivatives, and decompositions. Section 4 covers eigenvalue identities. Essential desk reference for ML researchers.
Compact review of eigenvalues, matrix calculus, and optimization for Andrew Ng's Machine Learning course.
Extremely popular "BAM!" style videos explaining PCA, eigenvalues in context of data science. Makes statistics fun and accessible.
A remarkable identity relating eigenvector components to eigenvalues of matrix minors, co-authored by Fields Medalist Terence Tao. Surveys appearances in random matrix theory, neutrino physics, graph theory, and numerical linear algebra.
Properties of eigenvectors of large random matrices and their role in combinatorics, theoretical computer science, and statistics.
Modern research on how to teach eigenvalues and eigenvectors using AI applications as motivation. Useful for educators.
Collection of research papers on eigenvalue problems across disciplines — from pure mathematics to physics and engineering.
Complete university-level linear algebra textbook in Japanese. Covers 固有値 (eigenvalues) and 固有ベクトル (eigenvectors) thoroughly.
University lecture notes designed for first-year students. Covers linear systems, matrices, determinants, eigenvalues, and diagonalization.
Step-by-step tutorial site explaining eigenvalue computation with examples — "Linear Algebra Explained So Even the Universe Can Understand."
Charming, beginner-friendly tutorial with cute illustrations. Covers eigenvalues and eigenvectors for first-year university students.
Lecture notes from Université de Montréal. Covers "valeurs propres" (eigenvalues) and "vecteurs propres" (eigenvectors). In French terminology, "propre" means "own" — same root as the German "eigen."
In Chinese, eigenvalues are called 特征值 (tèzhēng zhí) and eigenvectors are 特征向量 (tèzhēng xiàngliàng). MIT OCW materials have been translated into Chinese. Search for "线性代数 特征值 特征向量" on Bilibili (Chinese YouTube) for hundreds of free video lectures.
In Korean, eigenvalues are 고유값 (goyugap) and eigenvectors are 고유벡터 (goyubegteo). Many Korean universities offer free lecture notes. Search KOCW (Korea Open CourseWare) for comprehensive Korean-language courses.
In Spanish, eigenvalues are "valores propios" (or "autovalores") and eigenvectors are "vectores propios" (or "autovectores"). Juan Carlos Ponce Campuzano and other Spanish-language educators provide free materials online.
In Arabic, eigenvalues are القيم الذاتية (al-qiyam al-dhatiyya) and eigenvectors are المتجهات الذاتية (al-mutajihat al-dhatiyya). Search YouTube for "القيم الذاتية والمتجهات الذاتية" for Arabic-language tutorials.
In German (where the term originated!), eigenvalues are "Eigenwerte" and eigenvectors are "Eigenvektoren." Jörn Loviscach provides an excellent free video series on YouTube covering "Lineare Algebra" in German.
India's National Programme on Technology Enhanced Learning offers complete linear algebra courses in Hindi and English. Covers eigenvalues with applications to engineering. Extremely popular in India.
Interactive tool: input any 2x2 matrix and watch the eigenvectors and eigenvalues update in real time. See how changing matrix entries affects the eigenvalues geometrically.
Enter any matrix and get eigenvalues, eigenvectors, and characteristic polynomial computed step-by-step with full working shown.
Type "eigenvalues {{4,1},{2,3}}" and get instant results with step-by-step solutions. Works for any size matrix.
Full textbook with embedded interactive demos. Drag vectors and see how they transform, watch eigenvalues change in real time.
Beautiful, interactive visual essay that lets you manipulate matrices and see eigenvectors in real time. One of the best visual explanations on the web.
72-page reference of every matrix identity you'll ever need. Section 4 covers eigenvalue relations, spectral decomposition, and matrix function identities. Essential desk reference.
Compact summary of eigenvalues, matrix decompositions, and their ML applications. Fits the essentials into a few pages.
Comprehensive reference article with formal proofs, history, applications, and links to related topics. Available in 50+ languages. A good starting point for deep dives.
🔗 English Wikipedia | 🔗 Japanese (日本語) | 🔗 Chinese (中文) | 🔗 French | 🔗 German
Compiled March 2026 • All links verified at time of creation • Most resources are free or open access
Tip: Start with 3Blue1Brown for visual intuition, Khan Academy for computation practice,
Gilbert Strang (MIT 18.06) for deep understanding, and Mathematics for ML for data science applications.
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