thank youu so much, after watching this video I finally can understand. This is the best explanation video about linear transformations I ever watched on youtube
Dr. Peyam, could you please make a new series about operators, which are widely used in Quantum Mechanics? You are very good at explaining complicated and abstract subjects. I am very curious to see where you would classify the topic. Does it belong in linear algebra, metric spaces, vector spaces etc.? It would be awesome.
Can you upload a video of these exercise please. T:R^3 to R^3 the linear transformation give by T (x1,x2,x3)=(3x1+x3, x1+x2, -x1). Define if it s possible a linear transformation T1:R^3 a R^3 such as T (T1 (0,2,1))= (-1,1,3); T1 (0,1,0)=(1,0,1) and Nu (T1)≠{0}.
I am not sure if that's allowed, but when I was asked to prove something is a linear transformation, I show that T(lambda * x + mu * y) = lambda T(x) + mu T(y) with lambda and mu constants. So you prove both additivité and multiplication par un scalaire. I know some people even shorten it to T(lambda*x + y) = lambda T(x) + T(y). Are there cases in which you can't do that directly? Because it seems so much shorter to do both at once.
Is it possible to do something like express x^2 + 4x + 6 +5y + 2y^2 + 3xy as some kind of matrix operation that starts with [(x),(y)]*? What options are there, if not, to do things like this? *I'm trying a new matrix notation where every row gets its own () when typed out, so in this case it represents a vertical vector.
oops, im stupid i thouhght that was just an exclamation point not a factorial lol. You cant really fiure it out with elementry functions, but you can extend the definition of a factorial into the gamma function, and u can just take derivatives from there, Γ(x)=(x−1)!, where Γ(x)=∫, from 0 to inf, of x^te^−tdt
Thanks,,Dr P! Very helpful, as usual. Slight problem with the viewing angle, tho, for the right half of the whiteboard. You're using a wide angle camera, so what you write farthest from the camera is a bit to compressed for easy reading. maybe position the camera so it's equidistant from L & R sides of the whiteboard? You still get away without having someone moving the camerato track you! Your handwriting is fine; just the viewing angle causes difficulty..
I was having a linear algebra class too. We we're on the topic Invariance. I was having a hard time understanding it. Do you have your version of teaching Invariance?
Isn't the second property you mentioned just the same as saying "a number can be added and also it can be multiplied" except multiplication can be proven through addition, right? T(2u) = T(u+u) = T(u)+T(u) = 2T(u), and so on
@@drpeyam provable by a summation series, sum 1+.4+.02... Fractions can be proven to obey the property that for 10U = K, that 10T(U) = T(10U) = T(K), and therefore T(0.1)=T(1)/10
@@drpeyam this does lead into another idea I had: matrices with matrices as elements. By all of the checks, you can have another matrix of matrices and apply them together all the same (vectors being 1-wide matrices)
My neighbours called police because i was loudly watching videos of Dr. Peyam's Show
.
The police arrested them.
hahahaha
Wow thank you for the explanation, you are the first person who I watched that actually explained it simply and thoroughly.
Also a linear combination goes to a linear combination, so it can be done with only one step, namely: f(ax + by) = af(x) + bf(y). ^_^
You can even drop that b.
Yeah, drop the b.
Omg I was just now watching 3b1b video on linear transformations and your video popped out of no where!! And I got to watch bprp's videos too!!
Your videos are so helpful, please keep making Linear Algebra videos! :)
I which I could like this video twice
Best linear Transformation explanation on RUclips!!!
Thank you Dr. Peyam. Genius
Such a colourful transformation. Made my day. You may though want a lesson from bprp in regard to the colour pen switch :).
thank youu so much, after watching this video I finally can understand. This is the best explanation video about linear transformations I ever watched on youtube
Dr. Peyam, could you please make a new series about operators, which are widely used in Quantum Mechanics? You are very good at explaining complicated and abstract subjects. I am very curious to see where you would classify the topic. Does it belong in linear algebra, metric spaces, vector spaces etc.? It would be awesome.
It rains in Southern California. I like your explanation and great unique sense of humour. Watching T.V. Well T of vector V.
Thanks !
TV time with T and U is best!
Que bonito
Es como estar viendo los simpson pero en una pizarra y ya no hay un Bart, solamente hay un buen profe escribiendo
Can't wait for some more. The matrix forms of linear transformations will be nice.
Thank you sooo much
0:20 namely 😊. I think in German we also use “namely” - nämlich, but not that often
Thank you really much !
I pity the fool who had an exam about this
Wow, BluePenRedPenGreenPen :-O
thanks a lot
Best explaination ever......
Excellent
Can you upload a video of these exercise please. T:R^3 to R^3 the linear transformation give by T (x1,x2,x3)=(3x1+x3, x1+x2, -x1). Define if it s possible a linear transformation T1:R^3 a R^3 such as T (T1 (0,2,1))= (-1,1,3); T1 (0,1,0)=(1,0,1) and Nu (T1)≠{0}.
I am not sure if that's allowed, but when I was asked to prove something is a linear transformation,
I show that T(lambda * x + mu * y) = lambda T(x) + mu T(y) with lambda and mu constants.
So you prove both additivité and multiplication par un scalaire.
I know some people even shorten it to T(lambda*x + y) = lambda T(x) + T(y).
Are there cases in which you can't do that directly? Because it seems so much shorter to do both at once.
You can do that, it’s just conceptually it’s better to do it separately
Is it possible to do something like express x^2 + 4x + 6 +5y + 2y^2 + 3xy as some kind of matrix operation that starts with [(x),(y)]*? What options are there, if not, to do things like this? *I'm trying a new matrix notation where every row gets its own () when typed out, so in this case it represents a vertical vector.
Yes, see the video on quadratic forms
Can you tell me please what's the derivative of X! ???
1
oops, im stupid i thouhght that was just an exclamation point not a factorial lol. You cant really fiure it out with elementry functions, but you can extend the definition of a factorial into the gamma function, and u can just take derivatives from there, Γ(x)=(x−1)!, where Γ(x)=∫, from 0 to inf, of x^te^−tdt
Yeah , I've tried it recently.....
Thanks,,Dr P! Very helpful, as usual. Slight problem with the viewing angle, tho, for the right half of the whiteboard. You're using a wide angle camera, so what you write farthest from the camera is a bit to compressed for easy reading. maybe position the camera so it's equidistant from L & R sides of the whiteboard? You still get away without having someone moving the camerato track you! Your handwriting is fine; just the viewing angle causes difficulty..
I’ve tried that, but then I cover up what I write. I’m experimenting with this a bit
Can you drag your camera atleast at second part of your bord.... because we cant see what is written on your right hand side...lol
But your vidio is really helpful...
I want to advise you to add more funny dialogue in your vidio to attract more students 🔥🔥🔥
But why linear tranaformation has exect correspondence to tensor(1,1)
I was having a linear algebra class too. We we're on the topic Invariance. I was having a hard time understanding it. Do you have your version of teaching Invariance?
Probably in 3 months or so
Good one, Dr. Peyam
:)
Anyone can put an example of function such that T(A+B)=T(A)+T(B), but T(aB) is not equal to aT(B) ?
Will Dr. Peyam make videos of second course level linear algebra?✌🏻
Yeah, in 3 months or so!
buti pa to yung teacher namin pucha hindi marunong magexplain
Who is Steve? :)
Isn't the second property you mentioned just the same as saying "a number can be added and also it can be multiplied" except multiplication can be proven through addition, right? T(2u) = T(u+u) = T(u)+T(u) = 2T(u), and so on
What about T(sqrt(2)u) ?
@@drpeyam provable by a summation series, sum 1+.4+.02... Fractions can be proven to obey the property that for 10U = K, that 10T(U) = T(10U) = T(K), and therefore T(0.1)=T(1)/10
For Rn it’s fine, but in general you don’t have limits of vectors
@@drpeyam this does lead into another idea I had: matrices with matrices as elements. By all of the checks, you can have another matrix of matrices and apply them together all the same (vectors being 1-wide matrices)
Can't wait for you to get to change of basis because that's what still bothers me
I was watching the TV 😅😅
Your camera is not straight Dr
I know!
🖤👏