Projection on y = 2x

Projection on line y = 2x

In this video, as a sequel to my reflection video, I calculate the formula of the reflection of a point about the line y = 2x. Of course one can do it more easily using multivariable calculus, but this is meant to be an application of change of coordinates, to illustrate the power of linear algebra. Enjoy!

[HDQuote]

Thanks again Dr Peyam.
I had this topic in linear algebra I and we still make heavy use of it in linear algebra II,
but your last video about relfection just made this whole topic *click* for me. And today I solved your question before watching the video and I saw that I was correct :)
Thank you so much again. You are the best prof! And I really love your enthusiasm!

[MrRyanroberson]

To scale any function by N across a line x sin(t) = y cos(t): z' = z e^-it [1, 0;0, N] e^it; reflection is N=-1, projection is N=0, the identity is N=1. Generally this resolves into the matrix: [cc-nss, cs-ncs; cs-ncs, ss-ncc], c=cos(t), s=sin(t). Another form is [cot - n * tan, 1-n; 1-n, tan - n * cot] * sin * cos

[michaelempeigne]

Why can one not take the distance from the line on one side and make it the same distance on the other side?

[SKARTHIKSELVAN]

Thanks for your video. Fluid mechanics heavily uses PDE. I am eagerly waiting for your PDE videos.

[WaveSound]

Hello professor. Can you find the 3D projection matrix for projection onto a line and a surface?

[sergioh]

Can you also cover orthogonal projections? Like when u project onto line orthogonally :)