It's a nice topic to get into if you have the time. Look at this diagram for example: en.wikipedia.org/wiki/Lp_space#/media/File:Vector-p-Norms_qtl1.svg
I am stumped by this analogy to a mirror. In a real, physical mirror, a beam of light reflects off of the plane of the mirror such that the angle of approach to the mirror is equal to the angle of departure of the reflected beam. I understand that you want to calculate the vector u. Since u is perpendicular to the desired plane, u defines the plane. But it makes no sense to me to call the resulting plane a mirror.
@@engineeringoyster6243think of y to be the mirror image of x, that‘s why the plane is a mirror. if you were to look at the mirror from any point on the side of x you would see the reflection of x as if it was y. basically y is a virtual object that you can see when placing the mirror as shown
Great geometric interpretation! Every video I have watched from these series really pays off!
1:42 did you just say endofunctor or net effect?
2:50
It seems that you wrote "u = v / ||v||_2".
What does the "2" mean?
I think that "u" is given by just dividing "v" by length of "v"
It means taking the 2-norm of v, which is defined as the square root of the sum of the squared elements of v. So it's indeed just the length
It's a nice topic to get into if you have the time. Look at this diagram for example: en.wikipedia.org/wiki/Lp_space#/media/File:Vector-p-Norms_qtl1.svg
I am stumped by this analogy to a mirror. In a real, physical mirror, a beam of light reflects off of the plane of the mirror such that the angle of approach to the mirror is equal to the angle of departure of the reflected beam.
I understand that you want to calculate the vector u. Since u is perpendicular to the desired plane, u defines the plane.
But it makes no sense to me to call the resulting plane a mirror.
@@engineeringoyster6243think of y to be the mirror image of x, that‘s why the plane is a mirror. if you were to look at the mirror from any point on the side of x you would see the reflection of x as if it was y. basically y is a virtual object that you can see when placing the mirror as shown