❖ One to One and Onto Functions (Isomorphisms) ❖

[GueVonez]

Sometimes during an exam question that idk, i just ask myself "what would Patrick do" sometimes it works

[TheFreezingTuberJosh]

Give this man an award. Been saving my ass in mathematics since years

[patrickjmt]

Sorry for all the sniffing in the video. My allergies make me want to die this time of year. My eyes almost swelled shut yesterday after a crazy reaction :(

[andyhype]

You deserve a star on Hollywood Boulevard. But it should be mathy like in the shape of a fractal or conic section.
Making good content that directly betters the community i.e. less sleep deprived students driving on streets, talking to normally rested people, and buying granola bars from vending machines at odd hours.

[RB]

Patrick, My deepest appreciation in your effort in as far as making these videos is concerned. Once again, thank you very much for this beautiful work. And sorry for your allergies.✌

[ericcannon]

I dont know how your channel has not shot off and gained tonnes of subscribers yet, your info is great and you have a gift through explaining "difficult" math is such a simple way! keep them coming!

[DavidLee-lxps]

Careful, there is a mistake in example 1 where the prof. forgot the 2 before x+2y (he wrote it as x+y). It changes the final vector of the transformation. The correct answer should be ((b+2a)/5), ((y2b-1)/5), obviously written as a column vector.

[mixalis]

Not to be a smartass or smth, but on 14:43 shouldnt be the x + 2y instead of x+y?? Again thanks for all the help, aprreciated it :)

[carashipley]

Your videos are always so clear and helpful! Thank you so much!

[stevefreed]

You should be a professor. This video was Supreme! My teacher sucks and spits out a bunch of theorems and general term formulas for linear algebra. You gave a picture.. and a picture is worth a thousand words. Thanks!

[lordofbitter]

i was dying due to these transformations there are good method out there but i couldnt grasp any of them .Thank you for your effort i now get it

[DarknessIsThePath]

So if I understood it correctly, 1-1 is always when R^n = R^n?

But it's always onto when R^m -> R^n when m>n but not when n>m?

[samuelkantor]

Awesome vid! Usually math vids don't help me learn but I loved this one! You're a legend

[nkhp]

YESSS. This is literally what I've been trying to understand for this final. THANK U <3

[abrarshaikh]

Sir! Please upload some videos on basics of tensor analysis &tensor calculus!!!

[ashleynerette]

I must be the only one confused by how you got two different transformations. When determining whether the function was 1-1, you initially had [2x-y over x+2y], but when you got to determining whether the function was onto it changed to [2x-y over x+y]. Can you please explain why it changed?

[ck-bynq]

Isomorphisms require more than being bijective in the linear-algebraic sense. Isomorphisms preserve the algebraic structure of the vector spaces, so we need more than just bijectivity. The map must preserve additivity and scalar multination in linear algebra. Of course, the requirements for a function to be an isomorphism can change, depending on the context (ex. an isomorphism is a bijective homomorphism in group theory).

[alhaithamaljabri]

Looking forward to seeing you hit the 1 million:]

[amanisaid]

Thank you, I got alot of benefits from your video

[jacksonmadison]

just row reduce the corresponding matrix and check for full column / row rank for injective / surjective respectively