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#determinant#linearalgebra#matrices

The determinant | Chapter 6, Essence of linear algebra

3Blue1Brown

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  • Recommended by 6 people: 6 on Hacker News.
  • A classic. People kept recommending it from 2020 to 2024.
  • May be out of date. Uploaded 10 years ago, in an area where tools change fast.

Beginner. No background in the topic needed.

5M views10 years ago6 recommendations

Computer scienceAI and machine learningMath for programmersMath for machine learning

A geometric explanation of the determinant as the scaling factor of area or volume under a linear transformation.

The determinant measures how much volumes change during a transformation. Help fund future projects: patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: 3blue1brown.com/ Full series: 3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. 3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Vietnamese: @ngvutuan2811 ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: goo.gl/WmnCQZ Various social media stuffs: Website: 3blue1brown.com Twitter: twitter.com/3Blue1Brown Patreon: patreon.com/3blue1brown Facebook: facebook.com/3blue1brown Reddit: reddit.com/r/3Blue1Brown

Why it's here

6 people recommend this

What people say. Widely recommended for providing the best intuitive, geometric understanding of determinants.

Chris_Newtonon Hacker News • Recommends

On “How to Understand Things”

…asic (by undergraduate standards) subject. I think it was probably a few years later, when I came across some of the same theory but in a much more practical context at work, that most of the connections in that equivalence theorem first “clicked”. Meanwhile, here is what a gifted presenter with the right illustrations can do in about ten minutes: link to this video The 2,000 or so substantially identical comments below that video are very telling. Given the understanding you’d get with that quality of presentation, the equivalences I mentioned above would have been obvious and constructing the proofs from first principles would have been straightforward.…

MaxBarracloughon Hacker News • Recommends

On “Expiring vs. permanent skills”

At the same time, universities could sometimes do a better job of letting students see why it's important to learn something. A great example is matrix determinant, which at first glance seems like an entirely arbitrary invention. The 3Blue1Brown YouTube channel does a great job with this, introducing the determinant in terms of geometry. It puts the geometric meaning of the function first, introducing the strange looking formula later on. edit And of course, it does all of this with excellent visualisations. link to this video

mekenon Hacker News • Recommends

On “2000 Years of Matrix Multiplication”

Determinants always fascinated me, partly (completely?) because of the cool sounding name. I always wanted to get intuition for them because their formula is so simple, which has always been deeply unsatisfying to me to just take on its face. This article got me searching for a 3blue1brown video on determinants and now my mind is absolutely blown! link to this video

traeson Hacker News • Recommends

On “Adventures in Probability”

The entire 3blue1brown series0 on linear algebra is well worth watching, it has really intuitive graphical explanations of a bunch of concepts. Here's the one on determinants in particular1. TL;DW the determinant represents how much you scale the area/volume/hypervolume (depending on dimension) of a shape by applying a matrix transformation to each point. 0 link 1 link to this video

JW_00000on Hacker News • Recommends

On “The paper that keeps showing up”

…see 4. Another great source of math visualizations is the YouTube channel 3Blue1Brown, in particular the series on linear algebra 5. (I didn't intuitively understand what a determinant represented or what the determinant of a transformation being zero really meant, until watching 6.) 1 link 2 link 3 link 4 link 5 link 6 link to this video…

3PSon Hacker News • Recommends

On “So what's the point of linear algebra, anyway?”

> The novel approach taken here banishes determinants to the end of the book. Big fan of this approach! Though I have warmed up to determinants ever since I saw 3Blue1Brown give a fairly intuitive explanation for them 0. I'm kind of curious as to how they covered eigenvalues/the characteristic polynomial without determinants. Maybe they just jumped straight to diagonalization? 0 link to this video

throwawaymathon Hacker News • Mentions

On “Relearning Matrices as Linear Functions”

I strongly disagree skipping determinants provides a more intuitive approach to linear algebra. I don't know your background, but I'd venture a guess you feel it does because the Laplace expansion formula for computing the determinant1 feels uninspired and out of place. The reason determinants are hard to teach (in my opinion) is because a rigorous derivation of their formula isn't possible without first teaching multilinear algebra and constructing the exterior algebra. Once you do those things, the natural geometric interpretation of the determinant basically falls onto your lap. But it's still very useful for e.g. computing eigenvalues and using the characteristic polynomial, so it's ta…