41. This rotation transformation can be represented in different ways, e . g ., as a rotation matrix or a quaternion. 42. To retrieve the axis angle representation of a rotation matrix , calculate the angle of rotation from the trace of the rotation matrix 43. To retrieve the axis angle representation of a rotation matrix, calculate the angle of rotation from the trace of the rotation matrix 44. The vectors and are indeed related by a rotation, in fact by the same rotation matrix which rotates the coordinate frames. 45. The transformation is a rotation around some point if and only if " A " is a rotation matrix , meaning that 46. Therefore, R = e ^ { Wt } is a rotation matrix and in a time dt is an infinitesimal rotation matrix. 47. Therefore, R = e ^ { Wt } is a rotation matrix and in a time dt is an infinitesimal rotation matrix . 48. The product of two rotation matrices is a rotation matrix , and the product of two reflection matrices is also a rotation matrix. 49. The product of two rotation matrices is a rotation matrix, and the product of two reflection matrices is also a rotation matrix . 50. It is common to describe a rotation matrix in terms of an axis and angle, but this only works in three dimensions.
