Linear Algebra 19k: Matrix Representation of a Linear Transformation - Vectors in ℝⁿ

[richardaneke]

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 🤬😡

[sirstroam]

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.

[TheGamer-ntew]

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.

[goodlack]

Thank you! Very informative video! Love it!

[joaopedronunes]

Great video! Very clear for a Linear Algebra I student! Keep it up!

[iilizjk]

Thank you. I have difficulty understanding my professor's lecture. This video helped me so much.

[antonellomascarello]

It's a pleasure to watch 🙂 Thank you Professor ☺️

[woofelator]

I'm so confused. What is happening at 6:06?

[ohmymahone]

why did he choose those numbers for the basis?

[alexbenjamin]

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.

[debendragurung]

5:50 ; it seems very counterintuitive that [T][B] is not Matrix of transformation in component space.

[ttvasakis]

thnkxs this helped me understand something confusing me in representation theory

[MrYuiagaraki]

I think the first matrix you show is also a matrix representation that has the standard basis :)
Anw tks for clearing my confusion :)

[TrojenMonkey]

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!

[tarkkoroglu]

you could give two different bases which would make it easier to understand. Thanks anyway

[akilan]

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?

[dana]

i assume this only works for lineair operators.