Transformation matrix with respect to a basis | Linear Algebra | Khan Academy
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- Опубликовано: 1 ноя 2024
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Finding the transformation matrix with respect to a non-standard basis
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We need examples bro...
U get wat u f***ing deserve brat
Lol
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).
Perfectly summed up! Thank you so much for this comment, going straight to my notes!
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
its not a waste of time, if you already have some idea behind it this video is incredibly helpful, because it helps you gain an understanding of what the numbers all mean. Just be patient, it'll come to you
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!
10 years later still saving undergrads from mental break down
Now this explained what I've been confused about for this whole semester! Thanks :)
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.
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!
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
The best thing I found on internet today.... Thanks... For making.. It...
Is it just me that I can't watch his video at regular speed? I always have it at 1.25x or higher.
i think its because he keeps repeating himself till he finishes writing the stuff
Yeah me too i actually use 1.5 or 1.75😂😂
I always put khan videos at 2x speed lol
Same here bro
u directly come on topic I thing u going to start with basic .....
You explained this twice as well as my university lecturer in half the time. Thank you!!!
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.
Absolutely brilliant. My concepts are rock solid now!
Cleared all my doubts. Nice explaination👍
thank you!
so so so much
Thank you!
Very helpful videos
MAAN! I love you from all my heart at the moment! you save LIVES!
Can you please explain a video telling all the def like span, basis, eigen vectors,values
Note:
Matrices D and A which satisfy the equation D = C^-1*A*C are called Similiar Matrices. Why "similiar"? Det(D) = Det(C)^-1*Det(A)*Det(C)= Det(A)
AMAZING....THANKS..
Fully understood
Masterfully taught man
Greattttttt video!!!!!!!!!
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.
Explained so well!
Awesome!!
Wow, Great lesson.
Thank. really makes things straight
I completely understand the concept, but I was looking for the actual transformation. One of the few Khan videos I've come across that let me down
But what if we’re considering more general vector spaces where the vectors may not be elements of R^n?
this is a mathematical topic, what relation does spelling have to correctness of an argument?
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)
Some tablets track motion above the pad, if it's close enough.
your mouse skills are incredible
Using an example wouldn't be hard, and it'd only makes it easier to understand. No idea why everybody NEEDS to make it sound as academic as possible, losing half of the crowd before even getting halfway through.
There should be a rule, that says that if you can't do basic spelling, you shouldn't be allowed to criticize other people's work.
Need example of question bro
That is so good. I more than thankfull for that.
Wow, you nailed it!
Is T(X) and [T(X)]B the same?
No (see explanation above)
8:49 Can somebody explain why A[nxn] is invertible if vector-columns are linearly independent?
it's a rule in LA that for a matrix to be invertible it should be a square matrix. a basis vector will be a basis for all of Rn only if it has n columns which are linearly independent making it a square matrix (there will anyways be n rows since we are talking about Rn space) and hence invertible.
Look into the Invertible Matrix Theorem and it's proof, and you will have a very detailed answer to your question.
The TLDR version is that there is a series of conditions that are either all true or all false regarding an nxn matrix, which we arbitrarily call "A". If any single condition listed in the theorem is true for A, then all of the conditions are true for A and A is invertible. Alternatively, if any single condition listed in that theorem is false for A, than all of the conditions are false for A and the matrix is not invertible.
As you might've guessed, one of the conditions is "The columns of A form a linearly independent set".
8:33
I have a question about the last equation, if D = Cinverse * AC, doesn't that amount to D= A times the identity matrix, b/c C inverse * C is the identity matrix?
I could not figure this out either... 7 years later.
Product of matrices is not commutative (in general), so nope, it's not the case
Do you have an example of this method?
Craxx Maxx Machaxx
this mean that A is the same in the standard and non standard coordinate
i am also thinking this.
I don't understand why [x]B is the same as [A*x]??? He says so 12:50 min in to the film, can someone pleas explain it to me?
Thank you, you are a great teacher! :)
korean translation has an error invertible is translated to not invertible instead of invertible
great video it helped me a lot :)
should be redone as keeps saying "this is this" but there is no manifestation on screen & he gets confused during important part
The best thing is,to eat pizza while watching these amazing videos.
But be carefull,dont forget the water,else you will regret it !!!
@andersbyintrnational he's not using a mouse lol
watching this video was a total waste of time because absolutely none of it made any sense. it is extremely difficult to follow along when everything is so abstract
I love you
If it's not a mouse, then what's with the cursor?
C의 역행렬이 존재하는데 왜 안한다고 번역을 ....
confusing still
He never lifts the pen out of the screen?
bnggsdd keras bet ni gurunya, arigatou, kamsamida, xie xie laoshi
The most confusing concept in my lifeeeeee!!!
I mean who the hell created this thing....
Sal, you should have been named Jesus.
wow this is awful, straight up just rambling for 18 minutes
Thanks a lot for this wonderful video.
amazing ...!