Transformation matrix with respect to a basis | Linear Algebra | Khan Academy

Finding the transformation matrix with respect to a non-standard basis

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[Ch]

Thanks, but I would really start with an example and show how the idea fits before explaining the theory behind it, I lost it about half way through this video

[RealMcDudu]

Excellent video. In short - to apply a transformation on a non-standard basis, you first move to the standard basis (C), then do the transformation (A), then move again to the non-standard basis (C-1).

[amberegbert]

I can't describe how awesomely helpful these videos are. A great supplement to taking a class, or reading a book on your own. I couldn't have made it through without your help on these. You rock!

[sungboklee]

Now this explained what I've been confused about for this whole semester! Thanks :)

[Jeff-wcho]

Thank you for maintaining as much abstraction as possible. Theoretical Linear Algebra courses are taught from this perspective, so it's very refreshing to see instruction without computation.

[yuchujian]

I couldn't believe there's such an understandable explanation after reading an extremely tedious textbook authored by a pretentious man...You explained it so well!

[TheDrunkMexicano]

Just so y’all know not everyone understands this way of teaching so can u add at least add 1-3 good examples with actual numbers after each short lesson then you’ll be able to hit a larger amount of ppl. Cuz this didn’t help me whatsoever. definitely a waste of time for me

[kkevinparkk]

Is it just me that I can't watch his video at regular speed? I always have it at 1.25x or higher.

[anweshkumar]

The best thing I found on internet today.... Thanks... For making.. It...

[samirpatil]

u directly come on topic I thing u going to start with basic

[PrUnEJuIcEtHeThIrD]

Thanks Sal. I might have to start watching your videos first, before attending my real class lectures or reading the book material. Would save me a lot of time on trying to "connect the dots" which class lectures and my textbook typically do a poor job of doing.

[abhinaygupta]

Cleared all my doubts. Nice explaination👍

[Rockyzach]

If [T(x)]B = [Ax]B = [x]B, then how does [T(x)]B = D[x]B at the top where you have it written in the second domain circle. That would mean [x]B = D[x]B which doesn't make any sense. Also I just realized you basically wrote this:

D[x]B = [T(x)]B = [Ax]B = [x]B therefore you are saying D[x]B = [x]B which doesn't make sense.

[devarasettysaikrishnavamsh]

Can you please explain a video telling all the def like span, basis, eigen vectors, values

[divyanshjain]

Absolutely brilliant. My concepts are rock solid now!

[MCCMcom]

You explained this twice as well as my university lecturer in half the time. Thank you!!!

[salehjamsaljames]

MAAN! I love you from all my heart at the moment! you save LIVES!

[arbitrarilyarbitrary]

But what if we’re considering more general vector spaces where the vectors may not be elements of R^n?

[ryanjacksonx]

I don't understand. Can a basis be thought of as where you are starting on the dimensional space? (As opposed to the origin assumed)

[nivshbibi]

Wow, Great lesson.
Thank. really makes things straight