Linear Algebra 15j: Example of Nonlinear Transformations of Functions

[AMADEOSAM]

Thanks! very good explaination and the topic is very interessting.

[srinsriram]

Clear explanation. The linearity is the property of the transformation T in relation to f, and not the function f in relation to x. I've gone through all the linear algebra part 1 videos and part 2 videos (till here, will finish it) and find this presentation novel and useful. A bullet-point summary of each of the videos would be useful (what the viewer should take away).

[OtterMorrisDance]

Is the last transformation meant to be f(x)+c ? Where c is a constant?

[ksfrqos]

can you explain in a more specific way what is the deiffrance between the first and the second transformation? that you draw on the board

i saw the video about the Dilation transformation and couldint figure out why T(x^2) = 4x^2 -4x + 1

why is that and how it is connected to the fact that this transformation is linear and the first transformation is not linear

[vijayshankar]

is there a nonlinear transformation for vectors

[InfiniteParadigm]

Hello I enjoyed you video very much and feel that it may have some connection to what I am trying to prove, but still can figure out how to address it. I am trying to find a transformation S(T(n)) = n where SoT = identity. However T(S(n)) is not identically equal to n and ToS is not equal to the identity. All I am given after that is that T is linear, 1 to 1 but not onto. And S is non-linear, onto but not 1 to 1. Does this make any sense to you.

[billchang]

again how to define a zero vector in this transformation is what puzzles me...

[gryphonvalorant]

WHY DID I WATCH 40 SECONDS OF ADVERTS FOR THIS

[Josdamale]

So, basically an Integration operation is nonlinear.