- #1
matrix_204
- 101
- 0
i was trying to figure out something that i didn't understand and the book doesn't have much examples of it either. My question is how do u know whether a transformation is a projection on a line, reflection on a line, or rotation through an angel? With T given. The questions i did from the book, i was able to find the line and reflection, since the same question was previously stated and i was able to do it, n got the answer from there, but didn't understand it.
Take T[x y]=1/2[x-y y-x] and by solving these i get [1 -1]/[-1 1] (this is not division, just goes at the bottom, its a 2x2 matrix, and the vectors r transposed) so by looking at this
[ 1 -1]
[-1 1]
how can u tell whether its a reflection, projection or rotation?
Similarly another result i got for another part was
[1/2 root3/2]
[root3/2 1/2 ]
i think this one is rotation but how can u tell?
Take T[x y]=1/2[x-y y-x] and by solving these i get [1 -1]/[-1 1] (this is not division, just goes at the bottom, its a 2x2 matrix, and the vectors r transposed) so by looking at this
[ 1 -1]
[-1 1]
how can u tell whether its a reflection, projection or rotation?
Similarly another result i got for another part was
[1/2 root3/2]
[root3/2 1/2 ]
i think this one is rotation but how can u tell?