Showing that an eigenbasis makes for good coordinate systems | Linear Algebra | Khan Academy

[@DelphianSociety]

Wow. I'm done. I (as a high schooler) decided to do L.A. as a distraction of high school math with the help of Khan and I've reached the end of my journey. I understand everything I've learned 100%, and I'm now ready to take on more difficult math subjects. I can't thank you enough for this gift you've given my, Sal!

[@davo1822]

nerd

[@__-aa]

Hijacking top comment point out the error at 4:10 First, what he says, which is correct: - Change of basis matrix, C, has all these [eigenvectors] as columns. But after that, he says and he writes, A = C-1 * D * C but the actual formula is A = C * D * C-1 "Downward arrows are C, upward arrows are C-1", unlike what he draws.

[@norwayte]

Good. Thank you for the pleading at the end. It would be good if YOU could do some concrete real day-to-day examples with the things you mentioned in your pleading. You have the gift.

[@Postermaestro]

Amazing series

[@NotmyYTchannel]

Thank you so much Sal!! is this end of the Linear Algebra? I hope you do more Linear algebra videos in the future!! there are still more things for my second year LA!

[@mabney11]

You make college professors look like dodo birds

[@Zerpentile93]

Much better than my book that just throws abstract formulas and definitions at me and expects me to just understand the logic behind everything.

[@FlareGunDebate]

This series is invaluable. Thanks, Sal!

[@ueiwqoak]

Looking at the diagram that's completed at @6:02 , my question is: what is the difference between a vector transformation and a change of basis? They seem to be represented by the same thing, a matrix, but sal uses them in a conceptually different way. So what is the conceptual difference between these two? I'm stuck here

[@ruolinjia286]

Change of basis is a vector transformation. It is just the specific transformation that maps your vector to another basis system. You can understand that vector transformation is a more general term.

[@RADIOACTIVEBUNY]

If it's possible to know a little too much, he has achieved it.

[@ycombinator765]

Wow you must be 10 yr older now!!! Hope you had success in your life. This is by far the earliest comment I have read on youtube

[@Waranle]

Thank you Sal :)

[@lhyx1990]

no example for eigenbasis? i don't understand where lamda 1->lamda n come from. aren't they suppose to be only one lamda for one Eigenspace? I'm so confused. help!!!

[@musaaddi]

great work 5 out of 5

[@dauntSilver]

@SuaveAccent its not too bad if you do it step by step :]

[@xardas1500]

Love it...;D

[@azestical6566]

The last one, once you are done this you have mastered math! Good job OwO

[@mkkrrccyy]

where is that zeros come from whyyyy zerooooo whyyyyyyyyyyyyyyyyyyyyy