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 :(
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.✌
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!
i'm surprised it has as many subs as it does to be honest, given that is a math channel and it is not 'personality' driven like the popular channels on youtube.
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.
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!
No, it isn't always 1-1 when you have the same domain and codomain, because you can have a constant function(transformation). I will give an example from algebra. f:R->R f(x) =5
Can someone confirm that Patrick is wrong to use x^3 as example of isomorphism as in linear algebra more is required than just proving bijectivity? Ie it must preserve the structure of the vector space IE it must preserve the the two rules of order not mattering in additivity and scalar multiplication?
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?
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.
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).
Guys i have a simpler way. Construct the associated matrix to f using canonical basis. Then if ker(M(f))=0v or in other words the dim(M(f))=0, then the mapping is injective. If the linear map say goes from V->W, then if the IM(f)=W or in other words the dim(Im(f))=dim(W). Enjoy :DD
To use that, prove that if det (A)~= 0 the transformation is 1-1. But i think even before that, first you’d have to prove that the range of the transformation= the column space for your ‘A’
![One to One and Onto Transformations: Transformations (2/4) [Passing Linear Algebra]](http://i.ytimg.com/vi/2FN7eMWz3vs/mqdefault.jpg)
Give this man an award. Been saving my ass in mathematics since years
Sometimes during an exam question that idk, i just ask myself "what would Patrick do" sometimes it works
This is how I got through calc 3 hahahaha
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 :(
STILL...YOU'RE THE BEST! Please don't stop!
Best out the best
This man deserves an Emmy award
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 :)
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.✌
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!
i'm surprised it has as many subs as it does to be honest, given that is a math channel and it is not 'personality' driven like the popular channels on youtube.
Your videos are always so clear and helpful! Thank you so much!
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.
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!
I LOVE THE WAY U SIMPLIFY THINGS
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
Awesome vid! Usually math vids don't help me learn but I loved this one! You're a legend
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?
No, it isn't always 1-1 when you have the same domain and codomain, because you can have a constant function(transformation). I will give an example from algebra.
f:R->R
f(x) =5
YESSS. This is literally what I've been trying to understand for this final. THANK U
IM BLACK HOW DO I TELL MY PARENTS
bro!! ur excellent in explanation!😎
thanks :)
Looking forward to seeing you hit the 1 million:]
me too! :)
Can someone confirm that Patrick is wrong to use x^3 as example of isomorphism as in linear algebra more is required than just proving bijectivity? Ie it must preserve the structure of the vector space IE it must preserve the the two rules of order not mattering in additivity and scalar multiplication?
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?
I'm confused about this too thought I was the only one
I'm pretty sure it was just an error in copying down the transformation.
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.
Thank you , I got alot of benefits from your video
In what folder can I find this video? Can’t find it in Linear Algebra. And do èou have more videos of Linear Algebra than the ones in that folder?
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).
Sir! Please upload some videos on basics of tensor analysis &tensor calculus!!!
Abrar Shaikh Yes, please! I would love to see a short introduction to the subject.
yes please i hope i would understand it as study it from indian mother book and get ok but i can't deal correctly with its indices
You are too great than my teacher.
Good day! I just want to ask why the second element transformation changed from x+2y to x+y when you were testing for onto. Thanks.
I also have this question. Perhaps it was a mistake?
What an amazing channel !
thank you! very helpful 😇
I loved the teaching
Thank u sir
do you have a video on one-to-one inverse function derivative?
Thanks a lot, your video really helped me.
Thanks -You do a good job
just row reduce the corresponding matrix and check for full column / row rank for injective / surjective respectively
Thank you for your videos
What do these symbols. ❖ represent? Is it the first video of the set?
nothing, just attention grabbers
The minuscule dislikes are from left hand writing :p great video
Guys i have a simpler way. Construct the associated matrix to f using canonical basis. Then if ker(M(f))=0v or in other words the dim(M(f))=0, then the mapping is injective. If the linear map say goes from V->W, then if the IM(f)=W or in other words the dim(Im(f))=dim(W). Enjoy :DD
Very clear ...Thank you.
IM BLACK HOW DO I TELL MY PARENTS
I believe to prove 1-1 you can also just find the determinant, and if det(A) DNE zero, it is 1-1.
To use that, prove that if det (A)~= 0 the transformation is 1-1. But i think even before that, first you’d have to prove that the range of the transformation= the column space for your ‘A’
Great video.
The second example could be solved by taking det of [2, 1, -1, 1] and concluding that since det is nonzero, the column space spans all R2.
In the first example, since det is nonzero, that implies that A is invertible and thus one to one.
Awsm...ur videos 👌👌
y = x^3 is one-to-one and onto but it is NOT an isomorph since it does not preserve linear combination ( f(1) + f(1) =/= f(1+1) )
So, is f : R→R; x→x² neither 1-1 nor onto?
correct
I love ur videos
IM BLACK HOW DO I TELL MY PARENTS
Er dette det samme som en-entydig?
The GOAT.
It's x+2y, not x+y
Thank you
Isomorphism=bijection
you are my lord
I thought the combination of injective and surjective is bijective
"Bijective" and "isomorphic" are the same, just like "injective" and "one-to-one" are different terms referring to the same thing
Tq so much
At what point do you run out of math to make videos about
never
Dude. Stop. Writing. 2's. as. small. a's. JUST STOP. why dont u write those 2's as the other normal 2's that u wrote?
oh come on man he's alright.
IM BLACK HOW DO I TELL MY PARENTS
IM BLACK HOW DO I TELL MY PARENTS
Is this supposed to be funny nowadays?
Conservative Developer it’s funny cuz black people are never this high in math