Linear transformations and matrices | Chapter 3, Essence of linear algebra

Quite possibly the most important idea for understanding linear algebra.
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Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Spanish: Juan Carlos Largo
Vietnamese: @ngvutuan2811

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Various social media stuffs:

[GeorgiTsvetkovsHangingBelly]

All of 3Blue1Brown videos should be stored in case of a global apocalypse

[meaninglessjunk]

3blue1brown is at the forefront of a revolution that he started. he’s innovating a new way to teach math with exceptional visual representations. so talented with the animations and so skilled at explaining. not all professors/teachers can perform what 3blue1brown can, but i think that’s where education is headed. absolutely exemplary job.

[bioshazard]

I recently picked up a book far above my level and this series is EXACTLY what I needed to comprehend the first page. Thank you for all your amazing content.

[Jleonpolanco]

I took Calc 1 - 4 and linear algebra on my way to an engineering & physics degree in college. I got what I'll call a "forced A" in all classes. I did not understand any of it, but I studied enough to apply the concepts in a test. Only when I studied physics did I understand enough of the math to apply it correctly to physics. After watching this video along with "The essence of calculus" series, I've realized that I didnt know anything.

These videos are gems, thanks a lot!

[brunoborgatti]

3Blue1Brown: "you can make high schoolers memorize this..."
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me, studying for my master degree in engineering: **looks away in shame**

[securedigit]

My life has been linearly transformed by 'shear' joy of watching this video!

[dark.E-]

It's a crime how they teach us linear algebra

[dabblingfrancis]

I've just finished the entire Essence of Linear Algebra series, a truly wonderful (re)introduction.

[AnanyaMuddukrishna]

You made me cry again. These are tears that flow when some obstacle in the mind is removed forever. Thank you, great teacher.

[alexsere]

whos the monster that taught me matrices but forgot to tell me about their origin and beauty

[deepjyotichakraborty]

Your videos are a gift to humanity, Grant. Words do not suffice to express how brilliantly you have brought focus on intuition behind mathematics, away from notations and terminologies. It is not hard to see that it is this intuition that helps one to think from first principles regarding a concept and further, derive the formulas. Thank you many times over and wish that you keep making videos like these!

[kkh]

I should've watched this when I was a sophomore. This 11-minute visualization is much more worthy than my last 6 years. Awesome.

[tppiotrowski]

This video finally gave me the intuition to explain why multiplying a vector by the identity matrix produces the same vector. It is because the identity matrix is a linear transformation which does not move i-hat and j-hat from their original positions. Great!

[krishtundwal]

i think a really really helpful thing in the future videos would be to add some practice questions for the people who really are learning from this playlist and not just watching it, i feel that the way to learn something like this is to get your hands dirty and make mistakes, and so a set of questions attached to each video would really boost the understanding and learning process. and i absolutely love this series, thank you so much!

[TheProblembaer]

When somone truly understands their subject they are really capable of explaining it in easy terms. For me, this is one of the signs of true academic mastery when you are able to explain things really understandable and to the point. Thank you 3Blue1Brown for making the lifes of many students so much easier.

Additionally I want to add, this is the way I always whished to understand math, not as a applications of rules, but understanding why that rules exist. These videos do a tremendous job of really intuitively explaining those rules.

[youceflabiad]

WTF, why would they teach me to multiply matices without telling me the point of it?? it just makes sense now and i instantly memorised it against my will, thank you

[KanjoosLahookvinhaakvinhookvin]

3b1br has to be one of the only animators out there who can say "you've gotta admit, watching [my animation] is pretty beautiful" in the middle of it and have no one disagree or annoyed.

[brandonwang]

When the alleged best math teacher in my school gets EASILY bested by a random talented dude online LOL. This channel is the best discovery on YouTube I've made so far. Your explanations and visuals combined simply beats any textbooks out there. Keep up the great work my man!

[takeiteasy]

After having already taken a basic course in linear algebra it finally all comes together. 1000 thanks your videos rock!

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After decades from the video revolution, now we finally encountered the start of 'real' video education revolution.