U don't know how to teach.... you're confusing people , you made me waste data for your stupid video....not everyone is as intelligent as you think, but you teach like everyone already knows it... please stop making videos and confusing people 🤬😡
hey man I know its been a year, but I can totally relate when I don't understand XD, but there are always tons of other sources and videos that can help teach the same subject.
I really thought you were joking at first, but turns out you are just rude. Dr. Grinfeld is an amazing teacher, he emphasizes intuition over formulas and facts. You are wrong on many levels!
ummm maybe it is not the problem with his teaching; but your attention span that is weakened by watching tiktok all day at this point that you cannot understand VERY CONCISE and COHERENT explanation. not sure if you understand what I'm saying...probably it's best you go back to the kindergarten. Simplified: stop assaulting people who are trying to make difference and make these videos for people that can actually study and improve on their results.
Hey studying for a final over this subject. I like the clear concise way you do your videos. Not too repetitive, yet slow enough that I can re-watch a couple parts and learn what a decomposition in order to understand the transformation.
Thanks a lot sir for such an in depth and detailed lecture. You made one of the hardest topic easier. The video isn't much confusing, when you focus on it and pay attention.
Finally after 3-4 re-watches and practice it made sense. You were explaining it very simply i don't know why i confused myself. Great lecture actually! Thank you
11:20 Let's assume you didn't have the result of the linear-transformation [1,2,3] -> [3, -1, 9]. How would you use this method to find the result? Seems like the "synthesis step" is completely reliant on knowing the result ahead of time, and making guessword with finding the right scalars to work with the basis to yield our desired results. That is to say, What would is the representation matrix good for? If we do have the expression of the linear-transformation, it seems like needless extra steps, when we have T: R^3 -> R^3 already handy. But if we don't have the linear-transformation....It doesn't seem like we want to use the rep-matrix either way! There seems to be just too many steps. At worst, we'd use the rep-matrix to find the equation for the linear-transformation, and then hope to never use it again!
there's no difference what the basis is as long as it does represent your space Rn. it could've well been the standard basis, that is (1, 0, 0)...(0, 0, 1)...would have worked the same way.
Why would one obscure the transformation by expressing it in terms of a basis? Given any vector in R^n, the initial matrix will transform the vector and produce another vector in R^n. Why is there a need to create a matrix which represents the transformation (which also happens to be a matrix)? In the case of polynomials and geometric vectors it makes sense, because it is an entirely new way of looking at the transformation.
Thank you for this question. In a generic situation, you are right. But I would say that in many situations, it's not "obscuring" but the opposite. For instance, if you choose an eigenbasis, with respect to which, the matrix representing the linear transformation is diagonal.
If I just use the transformed basis vectors as the LT, then apply transformation to the vector [3,-1,0], I get the same result. What is the benefit of expressing the LT as components?
+Akila N Are you essentially asking, what's the point of translating everything into component space if you can work with LT transformations directly? One of the answers is, the LT may end up being much simpler (e.g. diagonal) with respect to a well selected basis (e.g. consisting of eigenvectors).
U don't know how to teach.... you're confusing people , you made me waste data for your stupid video....not everyone is as intelligent as you think, but you teach like everyone already knows it... please stop making videos and confusing people 🤬😡
hey man I know its been a year, but I can totally relate when I don't understand XD, but there are always tons of other sources and videos that can help teach the same subject.
I really thought you were joking at first, but turns out you are just rude. Dr. Grinfeld is an amazing teacher, he emphasizes intuition over formulas and facts. You are wrong on many levels!
ummm maybe it is not the problem with his teaching; but your attention span that is weakened by watching tiktok all day at this point that you cannot understand VERY CONCISE and COHERENT explanation. not sure if you understand what I'm saying...probably it's best you go back to the kindergarten.
Simplified: stop assaulting people who are trying to make difference and make these videos for people that can actually study and improve on their results.
Hats off for the professor not just for his insightful videos but for pinning this comment as well....
Common man, just dislike and get out, why you're acting like a kid.
Hey studying for a final over this subject. I like the clear concise way you do your videos. Not too repetitive, yet slow enough that I can re-watch a couple parts and learn what a decomposition in order to understand the transformation.
How did you do on your final?
@@MathTheBeautiful I don't remember. I did end up passing the class and getting my degree though.
Thanks a lot sir for such an in depth and detailed lecture. You made one of the hardest topic easier. The video isn't much confusing, when you focus on it and pay attention.
Finally after 3-4 re-watches and practice it made sense. You were explaining it very simply i don't know why i confused myself. Great lecture actually! Thank you
This one takes a while to get used to.
Great video! Very clear for a Linear Algebra I student! Keep it up!
Thank you. I have difficulty understanding my professor's lecture. This video helped me so much.
I'm so confused. What is happening at 6:06?
Are you asking about the decomposition of the image with respect to the basis?
It's a pleasure to watch 🙂 Thank you Professor ☺️
Thank you!
Thank you! Very informative video! Love it!
5:50 ; it seems very counterintuitive that [T][B] is not Matrix of transformation in component space.
Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.
11:20
Let's assume you didn't have the result of the linear-transformation [1,2,3] -> [3, -1, 9]. How would you use this method to find the result?
Seems like the "synthesis step" is completely reliant on knowing the result ahead of time, and making guessword with finding the right scalars to work with the basis to yield our desired results.
That is to say,
What would is the representation matrix good for? If we do have the expression of the linear-transformation, it seems like needless extra steps, when we have T: R^3 -> R^3 already handy.
But if we don't have the linear-transformation....It doesn't seem like we want to use the rep-matrix either way! There seems to be just too many steps. At worst, we'd use the rep-matrix to find the equation for the linear-transformation, and then hope to never use it again!
why did he choose those numbers for the basis?
Arbitrarily. The approach works the same way in any basis.
there's no difference what the basis is as long as it does represent your space Rn. it could've well been the standard basis, that is (1, 0, 0)...(0, 0, 1)...would have worked the same way.
Why would one obscure the transformation by expressing it in terms of a basis? Given any vector in R^n, the initial matrix will transform the vector and produce another vector in R^n. Why is there a need to create a matrix which represents the transformation (which also happens to be a matrix)? In the case of polynomials and geometric vectors it makes sense, because it is an entirely new way of looking at the transformation.
Thank you for this question. In a generic situation, you are right. But I would say that in many situations, it's not "obscuring" but the opposite. For instance, if you choose an eigenbasis, with respect to which, the matrix representing the linear transformation is diagonal.
Nice question. I would expect to read a book about it. No reference here plus no experience ] EDIT: Doubt Solved till lecture 19t
Great video, thank you
what is happening at 6:48 ?
Alternative arithmetic
Excellent teaching! Thank you.
I liked it, Thank you so much
i assume this only works for lineair operators.
thats what the video title says
If I just use the transformed basis vectors as the LT, then apply transformation to the vector [3,-1,0], I get the same result. What is the benefit of expressing the LT as components?
+Akila N Are you essentially asking, what's the point of translating everything into component space if you can work with LT transformations directly? One of the answers is, the LT may end up being much simpler (e.g. diagonal) with respect to a well selected basis (e.g. consisting of eigenvectors).
thank you so much this was so helpful
Glad it helped!
you could give two different bases which would make it easier to understand. Thanks anyway
thnkxs this helped me understand something confusing me in representation theory
nice explanation
I think the first matrix you show is also a matrix representation that has the standard basis :)
Anw tks for clearing my confusion :)
huh