Change of basis | Chapter 13, Essence of linear algebra

How do you translate back and forth between coordinate systems that use different basis vectors?
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Thanks to these viewers for their contributions to translations
Vietnamese: @ngvutuan2811

[CStrikr]

I love how when the "teacher' @5:30 asks "You've all watched chapter 3, right?" the Pi Creature to the left rolls his eyes trying to look normal with that stressed out facial expression, like "nope.." Very meticulous with these videos I love it.

[PrimaSiPensaDopoSiFa]

You are playing an important role in my formation. Thanks.

[kolotoure]

I study in Norway, and our professor recommended this series as a supplement resource to the course. I was pleasantly surprised he's humble enough to do so.

[JackPunter]

Storytime: I watched this video about 6 months ago for the first time when I stumbled across this channel and decided to watch this series (as well as most of the other ones) and I thought. that's cool, doubt I'll ever need to use it but its still cool. Until today, I'm working on a University project where we essentially have to triangulate the GPS coordinates of an object based off of compass bearings from known locations we are doing this over a small enough area that the "grid" of GPS coordinates can be considered rectangular (so the maths is still linear algebra) but sadly stuff doesn't work as nicely as with square coordinates. so after a good few minutes of thinking about how to solve this problem and, getting very frustrated, I took a 5-minute break to rest the brain and BAM!!! I remembered this video and thought "I can just change the base to a rectangular one". So here is a massive thank you for this amazing content that I watch in passing and then next thing I know. I'm thinking back to it using it in a real-world engineering problem, Keep it up dude Love the content. really wish I could support you on Patreon

[davidk]

It's amazing that a free collection of about a dozen short YouTube videos is incomparably more effective than any semester long university course.

[paradoxicallyexcellent]

Grant. Beautiful. Literally tears in my eyes. This isn't just a math education video. It's a valuable contribution to humanity.

[qasidsaleem]

I was a student who had 91/100 in Linear Algebra but had no intuition about what was actually behind 2-3 pages long answers. After watching this series, my beliefs about linear algebra have completely changed. I owe you a lot!

[david]

Chapter 9: Change of Basis
Chapter 10: Eigenvectors and Eigenvalues
...
...
Chapter 100: A full derivation of Einstein's Field Equations, with applicable examples in cosmology

Please?

[felipegonzalezlelong]

All of these videos are such an emotional rollercoaster for me. First the confusion, then the illusion of understanding, then frustration when I realize I didn’t, finally the absolute awe when I get it and see the beauty behind it all

[omedelbums]

Why does Jennifer has to be so complicated tho

[dragoncurveenthusiast]

6:44 This is what helped me solve the apparent "backwards" translation:

Consider Emily, who uses a (1D) grid which is 5 times larger than ours (her 1D basis vector is 5). So, all of her coordinates are 5 times smaller than "our" coordinates for the same vector.

1 * 5 = 5
vector in her language * her basis in our language = vector in our language

5 * 1/5 = 1
vector in our language * inverse of her basis (in our language) = vector in her language

[ash_engineering]

Sir you are undoubtedly the best teacher i ever had...

[reezis]

Finally a teacher that describes every part distinctly and coherently. My teacher just showed the algebraic part of changing basis but you put everything into reality now I fully understand. You are a genius

[KampfKeks]

You sir, have no idea how much this helps me as a math undergrad. I recommend the Calculus series to anyone who listens to me for more than 2 minutes. Now this one on Linear Algebra is a great help for me. You're doing great work and you should know that!

[arturtamborski]

Those animations are most important part in Your videos. You are doing great job in explaining but animations deserve its own appreciation.

[passionatelaugh]

I am grateful that my professor made a terrible job so I could discover this masterpiece.

[peanutbutterjelly]

I have seen this video many times in the past.
Now I am in my Ph.D. and whenever I need to refresh my understanding, I always think of Jennifer.

Thank you for introducing the ever-complicated Jennifer.

[michelleh.]

Ok, these videos honestly save my life. I can't believe linear algebra isn't taught this way all the time! 😲

[michaelppaull]

This series has been the perfect addition to my current linear algebra course at my university. The lectures are mostly just definitions and lots of jargon and its very difficult to grasp on its own. The visual representations in these videos along with your explanations have really opened my mind up to this beautiful subject and I am very grateful.

[Titurel]

You are making what was my least favorite math subject one of my favorites!