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Vectors: the first step in linear algebra
Study materials
English notes, a quiz, flashcards and a PPT outline are available below the player.
Slides are a PPT outline, not a finished slide deck.
Overview
The first chapter of 3Blue1Brown's Essence of Linear Algebra series, introducing vectors with animated geometric visuals. It begins a series that builds intuition for linear algebra from the basics.
Why HN discusses it
HN's go-to recommendation for learning linear algebra intuition, repeatedly credited with making concepts click and complementing textbooks.
Before you watch
No advanced mathematics is required. Familiarity with coordinates helps; this short lesson suits learners seeking visual intuition before algebraic calculations.
A way to study this video
Draw the same vector as an arrow and a list of components. Explain what stays the same when the arrow moves, then use the practice questions to check that distinction before the next chapter.
Newest first
In discussion: Immersive Linear Algebra Book with Interactive Figures
3Blue1Brown[1] has opened my eyes on the intuitive understanding of linear algebra, many, many years after taking a first course in linear algebra, which left me completely mystified. [1] [VIDEO]
In discussion: An Illustrated Introduction to Linear Algebra, Chapter 2: The Dot Product
If you actually want to learn linear algebra, don't use this blogpost. It's real weaksauce compared to the wealth of free information and resources available online. Firstly, the real illustrated guide to linear algebra is the youtube series "The Essence of linear algebra" by 3blue1brown[1]. It has fantastic visualisations for building intuition and in general is wildly superior to this, which seems fine but…If you actually want to learn linear algebra, don't use this blogpost. It's real weaksauce compared to the wealth of free information and resources available online. Firstly, the real illustrated guide to linear algebra is the youtube series "The Essence of linear algebra" by 3blue1brown[1]. It has fantastic visualisations for building intuition and in general is wildly superior to this, which seems fine but extremely superficial. If you're done with 3b1b and want to take things further, then the go-to is the excellent 18.06SC course by the late and legendary Gilbert Strang. It's amazing, it's free. [2] Still want more? OK now you're talking my language. If you are serious about linear algebra (Up to graduate level, after that you need something else) then you want the book "Linear Algebra Done Right" by Sheldon Axler. It's available for free from the author's website[3] and he has made a bunch of videos to supplement the book. There's also an RTD Math full lecture series[4] that follows the book and he explains each thing in a lot of detail (because Axler goes fast , so it's beneficial to unpack the concepts a bit sometimes). [1] [VIDEO] [2] [LINK] [3] [LINK] and [LINK] [4] [LINK]
In discussion: Adventures in Probability
The entire 3blue1brown series[0] 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 particular[1]. 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] [VIDEO] [1] [LINK]
In discussion: Linear Algebra Done Right [pdf]
Linear Algebra Done right did not help me try to demystify linear algebra. Quite the contrary. It is the Youtube channel 3Blue1Brown[1] that gave me an intuition of what linear algebra was about, and I am forever thankful to him. Watch it and if you are a teacher, don't be a smug "formalist". [1] [VIDEO]
In discussion: How do I relearn mathematics for machine learning?
3blue1brown's visualizations made a lot of things click for me, years after learning algebra and calculus. In my opinion they're the perfect companion to a more formal study with textbooks. Playlist for linear algebra: [VIDEO]
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