Linear Transformations

Showing something is a linear transformation

[DonSolaris]

My neighbours called police because i was loudly watching videos of Dr. Peyam's Show
.
The police arrested them.

[hofstra]

Wow thank you for the explanation, you are the first person who I watched that actually explained it simply and thoroughly.

[SmileyHuN]

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). ^_^

[georgiasonter]

Your videos are so helpful, please keep making Linear Algebra videos! :)

[wolframalpha]

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!!

[jstroner]

Best linear Transformation explanation on YouTube!!!
Thank you Dr. Peyam. Genius

[KidNamedVashin]

I pity the fool who had an exam about this

[aiupal]

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

[jorgejoeinfantesantacruz]

Que bonito
Es como estar viendo los simpson pero en una pizarra y ya no hay un Bart, solamente hay un buen profe escribiendo

[frozenmoon]

Such a colourful transformation. Made my day. You may though want a lesson from bprp in regard to the colour pen switch :).

[dariosilva]

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.

[mamadetaslimtorabally]

It rains in Southern California. I like your explanation and great unique sense of humour. Watching T.V. Well T of vector V.

[mathemitnawid]

0:20 namely 😊. I think in German we also use “namely” - nämlich, but not that often

[vanessakitty]

Can't wait for some more. The matrix forms of linear transformations will be nice.

[brunogreco]

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}.

[ELECTRONICAFISICA-UIB-]

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) ?

[jaydeeppatel]

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

[mustafahasan]

Can you tell me please what's the derivative of X! ???

[aleksanderaksenov]

But why linear tranaformation has exect correspondence to tensor(1, 1)

[PackSciences]

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.