Changing Between Two Bases | Derivation + Example
We previously saw the "Change of Basis" formula between a nonstandard basis and the standard basis. In this video, we look at how to change between two different nonstandard bases. Indeed, we derive a single matrix, called the Change of Basis Matrix, that is simply the product of two others: converting from the B basis to the standard basis, and converting from the standard basis to the C basis. That lets us go from the B to the C directly.
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Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master math means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
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Пікірлер: 52
Literally the best algebra channel on youtube
imo by far the best vid on youtube explaining the concept of a change of basis. I had trouble understanding this for a really long time and now all of a sudden , I do, so thank you!
You are the guilty of my healthy mental state and 8hr of sleep. Thank you !
I am watching all your LA videos ! They're really helpful
I didn't understand how the change of basis matrix was a thing until you showed these formulas that my prof shorthanded during lecture. Thank you!!
This is by far the best and most intuitive explanation on basis change.
I think these series are so great! I`ll share it with my friends I hope u extend your playlists to more math branches in the future. ^_^
Thank you very much on this series and this particularly video. Excellent and very clear stuff.
Thank you so much sir. your teaching method of actual geometrical visualization is great. Everyone should follow this. I am really grateful to you.
Your videos on Linear Algebra are the best ones on KZread. Thanks. :)
@DrTrefor
3 жыл бұрын
Glad you like them!
Man i can see the passion and love of math in your eyes when you explain!THANK YOU❤!
This is the best algebraic demonstration of basis change I have ever seen.
Could not be any better Dr Bazett
I have been struggling one day figuring out what the hell is going and luckily I see this video, you save me alot of times, thank you
27k view only?? By far the best video explaining change of bases to me. After this video all kinds of derivations and applications become apparent.
Just incredible. Thank you so much.
Thank you so much. The equation just dissolved all of the fog about the changing bases within my brain
Great as always Mr. Bazett!
Very nice and easy way to teach thank you Sir.
Thank you. Really. This is such an amazing video, short, concise, brings reminders of how to think, you show your own reasoning, the symbols are not some confusing ai and aj type of thing, and there are examples. Keep powering through maths!
@DrTrefor
3 жыл бұрын
Glad you enjoyed!
Man all your videos have helped me through all my mathy courses they are excelent
Thanks for the explanation dr. Greetings from colombia.
thanks for THE GREATEST lecture!
Very good explanation. Thanks
Very good expliation!
dude god bless you
I love this explanation
Love you Trefor!
thank you so much
very nice explanation!
Wow this is so helpful 👍🏻👍🏻👍🏻
awesome ❤❤
Thankyou sir
Whenever I have a new basis then can I always think about the new basis vectors as written in the standard basis. Essentially, can the standard basis be the “master basis” where everything can be though of through that basis?
good good subscribed
2 days of my life explained in 1 video
im finally getting linear algebra. probably not in time for my exam but for the retake :D
If inverse does not exist transformation is not possible, is it ?
If the commutativity of matrix multiplication matters for what it is, how is equation 6:15 valid? inv(Pc)*(x)b = inv(Pb)*(x)c is what I'm talking about, with inv() as the inverse notation (as in matlab command) Edit: I'd like to add tho, I never understood change of basis until I watched this video. So this was very good and your work definitely helped me understand linear algebra much better!! Thanks!
If you see, these topics are intuitive but it exposes a flaw in our education system. I should get my degree from KZread
Great teacher, why is he in such a rush?
I'm kind of confused because as far as I understand this is totally inapplicable in more abstract vector spaces such as R[X]. Did you explicitly mention in the series that you're going to focus on coordinate spaces?
@DrTrefor
Жыл бұрын
Indeed, this linear algebra playlist is intended entirely in R^n. Of course, a lot of things extend pretty similarly to other vector spaces, but that is beyond the scope of this particular series.
LOL, this is *so* confusing… Haha 😅😅😅 I feel extremely rusty!
hero
The shirt button is open. Anyway, super thanks sir.
A P(iece) of C(ake)
Ace of base?
we all know what Pc does... checking someones privilage
@marcuswortmann9664
Жыл бұрын
and check on someones micro-aggresions