corresponding to the point (— 2.8227, — 0.1917,0) is unchanged by the transformation. Another eigenvector, does not correspond to a point since its last value is zero, but this vector can be multiplied by any real scalar k and added to the original point to find another point that is unchanged by the transformation. This can be confirmed as follows:
viewed as a rotation of — 18.8571° around the axis ( — 2.8227, — 0.1917,k), where k can be any real value. In addition, an orthogonal translation of — 6.0943 units along the newly defined z-axis must be applied to account for the other component of matrix V.
Points and vectors in the newly defined coordinate system can be converted back to the original coordinate system using the matrix U.
The point (— 2.8227, — 0.1917,0) is the point on the rotational axis closest to the origin and corresponds to the point ( — 1.9053, 2.0556, — 0.3853) in the original coordinate system:
Was this article helpful?