Vectors | Chapter 1, Essence of linear algebra

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] ▶ this video

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] ▶ this video [2] link [3] link and link [4] link

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] ▶ this video [1] link

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] ▶ this video

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: ▶ this video

Essence of linear algebra is an absolutely wonderful series. It gave me an intuition of the subject in a matter of hours in way years of university didn’t do. ▶ this video

Here's another vote for 3Blue1Brown's series on linear algebra [1]. Spending a few hours on this series will easily save you dozens of hours when going through a comprehensive LA textbook. [1] ▶ this video

For anyone wondering what 3Blue1Brown is, it's a top Youtube channel with very nicely made explanatory videos for math. The videos on linear algebra in particular are worth it, especially if you do any sort of machine learning: ▶ this video . The author of the channel is Grant Sanderson. He has recently given a talk at SIGGRAPH 2021: link . As part of developing his Youtube channel, he has written and open-sourced manim, a library for programatically generating animations written in Python: link .

I strongly recommend 3blue1brown's intro to linear algebra[0] for quick intuitions, followed by Gilbert Strangs MIT Open Course[1][2] for (much) deeper detail. Strang is a genius, but Sanderson's graphics and intuitions can be helpful early on. [0] ▶ this video [1] link [2] link

This is ok but nothing is as intuitive as 3B1B's series on YouTube that has been posted hundreds of times on HN [0]. Linear algebra is really about linear transformations of vector spaces, which is not captured in this blog post. [0] ▶ this video

If you want to get an intuitive, visual understanding of linear algebra -- including eigenvectors/eigenvalues -- 3blue1brown's playlist on the subject is just ... perfect. ▶ this video

3Blue1Brown's Essence of linear algebra series is the go to place for learning this material. I've included the link to the series below so people don't get lost in all his other wonderful videos along the way. ▶ this video