Finding the matrix of a linear transformation and figuring out if it's one-to-one and/or onto. Check out my linear equations playlist: • Linear Equations
Just wanted to say thank you for all the linear algebra videos, Dr. Peyam!
@drpeyam
5 жыл бұрын
Thanks so much!!!
@santiagocolt2574
3 жыл бұрын
Instablaster...
@pepperbox2282
10 ай бұрын
my kind sir, I don't know why this was as hard to find as it was as it is a simple concept. You explained it beautifully, thank you.
@itsguy695
2 жыл бұрын
Thank god you exist, the way most people teach this is so obfuscated 😭
@drpeyam
2 жыл бұрын
Thank you!!!
@thedoublehelix5661
5 жыл бұрын
For onto, I think about the space of all inputs (x) as an island and the space of all outputs as another island. I imagine the transformation A to take anyone in (x) to a place in the outputs (b). And onto means that there will always be an inverse bridge that takes anyone in (b) to a place in (x).
@anthonygracioppo6337
Жыл бұрын
Bro thank you so much, been struggling to figure this out for my exam, I kept getting confused with my teacher's terminology. THANK YOU!!!
@kamrulhassan7157
3 ай бұрын
You are a great teacher sir ❤️❤️
@drpeyam
3 ай бұрын
Thanks a ton!!
@TheTim466
5 жыл бұрын
Why do English speakers always use "1 to 1" and "onto"? Here we always say injective and surjective (and bijective instead of "1 to 1 and onto" for that matter). Just something I always wondered.
@neilgerace355
5 жыл бұрын
That's proper mathematical English too, but we English speakers are sometimes lazy :)
@sugarfrosted2005
5 жыл бұрын
Beyond linear algebra it's pretty much never used. Though I can defend 1 to 1 because it's often useful to talk of " to ". Though the phrase "maps onto" instead of "maps surjectively" is still used.
@maryxue5532
Жыл бұрын
Thank you! Awesome video
@ldb579932
4 жыл бұрын
Would this be a valid and simpler argument without considering the associated matrix A at all? Every output of T has 0 in the first coordinate so it's clearly not onto. Furthermore, it's range is at most 3 dimensions so it must be many to one.
@drpeyam
4 жыл бұрын
Of course
@TheMauror22
5 жыл бұрын
Can you please prove those alternative definitions of one to one and onto that you talked about? I'm intrigued!!
@drpeyam
5 жыл бұрын
T is 1-1 if x not equal to y implies T(x) not equal to T(y) T is onto B if for every b in B there is x with b = T(x)
@IP__12318
2 жыл бұрын
You are just amazing!Thanks a lot!
@benjaminbrat3922
5 жыл бұрын
Yay! Great video as always! The answer to those 2 questions is very dependent on the space considered. If your image space is {(0,x,y,z) l (x,y,z) ∈ lR^3}, then the results differ, don't they?
@drpeyam
5 жыл бұрын
Definitely!
@zhansayamaksut6299
5 жыл бұрын
Hello! Thank you so much for your video, that was really helpful! But I have one question when mentioning the pivot positions in the rows and columns, do we consider only the coefficient matrix or the augmented matrix?
@drpeyam
5 жыл бұрын
Usually the coefficient matrix
@DiegoMathemagician
5 жыл бұрын
Hi Dr. Peyam! I haven't seen all your linear algebra videos; can you tell me if you already made a proof for the Rouché-Capelli/Kronecker-Capelli/Rouché-Fontené/Rouché-Fröbenius theorem? (All the names are different ways for naming the same theorem). If not, can you make a proof? I really need it to understand my classes. Thank you very much if you read this.
@drpeyam
5 жыл бұрын
I’ve never heard of those theorems 😱
@DiegoMathemagician
5 жыл бұрын
@@drpeyam It's funny because in Spain, where I live, is like a fundamental theorem, however, I always prefer to search math content in English but I barely see videos about that theorem. I would be so pleased if you dedicate one video for it :)
@drpeyam
5 жыл бұрын
What does the theorem say?
@DiegoMathemagician
5 жыл бұрын
@@drpeyam It is a great theorem for discussing linear systems of equations with some parameters. Let A be the coefficient matrix and A* be the augmented matrix of a system of linear equations; let n be the number of variables the system has. Then the theorem states that if rank(A)=rank(A*)=n, the system has exactly one solution; if rank(A)=rank(A*)
@drpeyam
5 жыл бұрын
Oh, I didn’t know that had a name! Maybe in the spring I’ll talk about that
@mostafaabboud5184
2 жыл бұрын
Well explained, thanks.
@omkarjagtap2351
Жыл бұрын
you are amazing
@sugarfrosted2005
5 жыл бұрын
I remember the theorem. For a linear map from a vector to itself: injective if and only if surjective. It's a consequence of the dimension. Of course, that's not really good to bring up yet, pedagogically.
@drpeyam
5 жыл бұрын
It’s a nice theorem, isn’t it?
@souvikroy8663
Жыл бұрын
Thanks sir ...
@hakbud
3 жыл бұрын
30 minutes away from the online exam, thanks apr 26th 2021 11:00am
@michaelbrowne4525
3 жыл бұрын
Thanks alot doc
@SmileyHuN
5 жыл бұрын
Hey Peyam! Would you do a video about the Steinitz Theorem? ^_^
Oh, I didn’t know that had a name! Yeah, probably, but only once I teach the proofy linear algebra course, so in 3 months or so
@SmileyHuN
5 жыл бұрын
@@drpeyam okay, sir ^_^
@postnubilaphoebus96
4 жыл бұрын
You are a treasure, Sir! Just read my textbook on linear transformations and your video perfectly complemented that.
@jerrychen9167
5 жыл бұрын
i love your watch
@drpeyam
5 жыл бұрын
Thanks! :)
@HettyPatel
3 жыл бұрын
tyty
@Fahodinho
3 жыл бұрын
thank youuu
@blooper6801
Жыл бұрын
I am having a stroke watching this in x1.5 speed because the lights keep getting brighter and darker
@drpeyam
Жыл бұрын
Sorry
@blooper6801
Жыл бұрын
@@drpeyam don’t worry Dr peyam, the video was very informative! It was my fault for trying to cram on x1.5 and x2 speed, not yours
5 жыл бұрын
Nice! I'm watching this video in Budapest, btw :D still waiting for your arrow's spike to show up somewhere on the sky above me :-O
@SmileyCarrot001
4 жыл бұрын
what jacket is that!!!!!
@drpeyam
4 жыл бұрын
Bprp gave it to me
@jonasdaverio9369
5 жыл бұрын
Would you mind, you all anglo-saxons people (you sure feel pointed out, Peyam 😂), using the right words someday? That means, injective and surjective
@jonasdaverio9369
5 жыл бұрын
Seriously, why are you still using those hideous names?
@drpeyam
5 жыл бұрын
That’s what they use in intro linear algebra classes
@gnikola2013
5 жыл бұрын
@@jonasdaverio9369 because they are beautiful
@remlatzargonix1329
5 жыл бұрын
Jonas Daverio .....okay, but could you please say that in English?
@Debg91
5 жыл бұрын
That's the terminology I learned in first course Calculus and Linear Algebra and the one I mainly use. One-to-One is also ok, but 'onto' hasn't even got a proper translation in my daily language. However as long as English is concerned, I think all these words are equally worthy. Probably 1-1 and onto are even more suitable for a first course
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