Question

My understanding of a rotation of a vector can be done by using a 2D rotation matrix as shown below,

R(theta )=[cos(theta) sin(theta)
-sin(theta) cos(theta)]

For example, if you rotate the vector

x=[1,1] by 45 degrees (clockwise), then the new vector is [sqrt2 0].

**My question is:**

If I have only initial and final coordinates of the vectors

The initial vector is, V = [1,1] and the final vector is, v = V+d = [sqrt2 0].

The displacement between these vectors is d = [sqrt2-1, -1].

Can I derive the final vector v with respect to displacement d(v)/d(d) to get the rotation vector?
A. but this returns a identity matrix.

If so, does [d(v)/d(d)] * d $ can be used to cross-check this?

Answer 1

It is difficult to solve.