Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
Why Hacker News recommends it
HN repeatedly names it the best, most intuitive explanation of eigenvalues, and a gateway to the whole linear algebra series.
What it is
3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.
Recommended by 6 HN commenters across 5 different months, 2016 to 2025.
What Hacker News said
Strong rec ivan_ah · 2016-10 · on “Meet the New Math, Unlike the Old Math”
On the topic of eigenvalues, this video is a very nice introduction: [this video] (the whole playlist kicks ass; highly recommended for anyone interested in "seeing" what linear algebra is all about)
Strong rec yamaneko · 2017-02 · on “The Essence of Linear Algebra [video]”
3Blue1Brown explanation of eigenvectors and eigenvalues is very insightful and intuitive [1]. One of my favorite videos from his channel is "Who cares about topology? (Inscribed rectangle problem)" [2]. They way a Torus and Möbius Strip come up as solution to the problem is so elegant. [1]: [this video] [2]: [LINK]
Strong rec raydiatian · 2022-11 · on “What is an eigenvalue?”
A far easier to digest primer on eigenvalues is available from 3Blue1Brown [+]. His presentation format is undeniably approachable, so much so that I think you could probably use it to teach linear algebra and eigenvectors to 9-year olds. [+] [this video]
Strong rec scmitton · 2022-11 · on “What is an eigenvalue?”
By far the best explanation of eigenvalues is found on 3blue1brown: [this video] Seriously, the course on the essence of linear algebra did more for me than my entire college linear algebra course. It's only a pity I discovered the videos at the end of my mechanical engineering degree and not sooner.
Strong rec mportela · 2025-03 · on “Statistical Formulas for Programmers (2013)”
Then definitely what 3Blue1Brown's video on eigenvalues and eigenvectors. [1] That's when I clicked to me! His entire series on Linear Algebra is incredibly well produced. [1] [this video]
Recommends steamer25 · 2018-05 · on “Eigenvectors and Eigenvalues (2015)”
3Blue1Brown has a good series on YouTube for building intuition in linear algebra: [LINK] In one of the last videos in the (relatively short) series, he discusses eigen-*: ~'eigen-stuffs are straight-forward but only make sense if you have a solid visual understanding of the pre-requisites (linear transformations, determinants, linear systems of equations, change of basis, etc.). Confusion about eigen-stuffs usually has more to do with a shaky foundation than the eigen-things themselves' [this video] All of the videos in the series, including this later one on eigen-things, focus on animations to show what the number crunching is doing to the coordinate system.