CSE 167 Lecture Notes - Lecture 3: Orthonormality, Rotation Matrix, Identity Matrix
16 Jan 2019
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Note: s x s-1 = i (identity matrix!) Note: only changes x-direction! (1 a, 0 1) (x y) x + ay. = (r cos cos - r sin cos , r sin cos - r cos cos ) = (x cos - y sin , x sin + y cos ) Advantage: any combination of transforms still retains a matrix! Option 2: inver each transform and swap order. Rows of matrix are 3 unit vectors of new coord frame. Can construct rotation matrix from 3 orthonormal vectors u = (cos , -sin ) ut = (cos -sin ) R = (ut, vt) (x) = (u x, v x) = (xu yu, xv yv) (x y) = (xux + yxy, xvx + yvy) New coord frame uvw taken to cartesian components xyz. Inverse or transpose takes xyz cartesian to uvw. Rotate by x, then y is not same as y, then x. Problem setup: rotate vector b by about a.
