I have a linear map R α = ( c o s α − s...
I have a linear map and the question goes like, how does transform a vector?
Can someone please help me?
Answer & Explanation
The comments above on the OP are good, but here's another perspective. How does change the length of a vector? It is easy to verify that
So that for some vector v we have . That is, is an isometry (it can't change the length of vectors). So if cannot change the length of a vector, it could only possibly rotate a vector. So what is this angle? We can compute the angle, , between and v by computing
I'll leave it to you to verify that this gives (mod or whatever)