rotation matrix

rows and columns are always mutually perpendicular (orthogonal) unit vectors

• a transformation matrix

• rotates a point counterclockwise by an angle θ around the origin.

• R is a normal matrix -

  • $R\cdot R^T=I$
  • $det(R)=1$

• Transpose of a rotation matrix produces a rotation in the opposite direction

• inverse is transpose

• orthonormal

https://en.wikipedia.org/wiki/Rotation_matrix

Conceptual explanation/derivation: TODO