Rotations/Angles naive/2,3/Section

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A rotation of the real plane around the origin, given the angle counterclockwise, maps to and to . Therefore, plane rotations are described in the following way.

A linear mapping

which is given by a rotation matrix (with some )with respect to the standard basis is called


A space rotation is a linear mapping of the space in itself around a rotation axis (a line through the origin) with an certain angle . If the vector defines the axis, and and are orthogonal to and to each other, and all have length , then the rotation is described by the matrix

with respect to the basis .