Youre really making me appreciate linear algebra a lot, after i somewhat struggled with it throughout my first semester in uni. Thank you very much for these videos! :DD
2:39 It is a neat fact, but it cannot be iff, and here is a counter-example: in RxR we have 2 subspaces that cannot be graph of any linear transformation from R to R, they are: {0}x{0} and {0}xR
A nice follow up would be the Closed Graph Theorem: let X and Y be two Banach Spaces and T:X->Y be a linear operator. Then, T is continuous iff G(T) is closed (on the product topology X x Y). Very cool.
Dr. Peyam I wanted to ask you how I can become better at understanding these proofs and such mathematical rigor and how I can implement this in a class. Do you have suggestions where I can start. I know you give really good explanations but at a fundamental level I don't seem to understand these proofs. What should I do and where should I start? Thanks for your videos!!!!!
I think that first you should start from scratch. You need to remember and understand definitions, in this video you should know what is a set, a function, linear tansformation, subspace ... Then, it is a matter of using the knowledge acquired.
@@gradecracker yes. This is how it works for me. Knowing the definitions makes the proof clearer. It is also important to understand what you are doing and looking in the proof.
This, and also I suggest to watch some of my earlier playlists (like Linear Equations or Matrix algebra), there I build up everything from the fundamentals on
Hi Dr. Peyam! I'm doing My major on mechatronic engineering and i'm coursing Linear Álgebra! This and more content about it are really worth it! Thanks a Lot. I would like to see videos for Cuadratic forms, Grand Schmidt and more please! Greetings
Youre really making me appreciate linear algebra a lot, after i somewhat struggled with it throughout my first semester in uni. Thank you very much for these videos! :DD
Dr. Peyam, you are gold!
Interesting. Almost on line ! I've finished all your videos that I wanted to see. Thank you very much.
2:39 It is a neat fact, but it cannot be iff, and here is a counter-example: in RxR we have 2 subspaces that cannot be graph of any linear transformation from R to R, they are: {0}x{0} and {0}xR
A nice follow up would be the Closed Graph Theorem: let X and Y be two Banach Spaces and T:X->Y be a linear operator. Then, T is continuous iff G(T) is closed (on the product topology X x Y).
Very cool.
You talked about it in the FA Overview, but didn’t get into the proof.
Yeah
Thanks. I saw your 100th video. Very interesting.
Lovely t-shirt!
Thank you ❤️
Dr. Peyam I wanted to ask you how I can become better at understanding these proofs and such mathematical rigor and how I can implement this in a class. Do you have suggestions where I can start. I know you give really good explanations but at a fundamental level I don't seem to understand these proofs. What should I do and where should I start? Thanks for your videos!!!!!
I think that first you should start from scratch.
You need to remember and understand definitions, in this video you should know what is a set, a function, linear tansformation, subspace ...
Then, it is a matter of using the knowledge acquired.
Azhar k Okay. So I should really focus in on the basic definitions and explore some of its properties and uses and then turn to these proofs.
@@gradecracker yes. This is how it works for me.
Knowing the definitions makes the proof clearer.
It is also important to understand what you are doing and looking in the proof.
Azhar k Thank you so much
This, and also I suggest to watch some of my earlier playlists (like Linear Equations or Matrix algebra), there I build up everything from the fundamentals on
Linear algebra 😊
Hi Dr. Peyam! I'm doing My major on mechatronic engineering and i'm coursing Linear Álgebra! This and more content about it are really worth it! Thanks a Lot. I would like to see videos for Cuadratic forms, Grand Schmidt and more please! Greetings
It’s all there already
but how do you plot it?
why T(0)=0?
Because it’s a linear transformation
T(0) = T(00) = 0 T(0) = 0
@@drpeyam thank you!!!