Reflection about x-axis: R2
Reflection about y-axis: R2
Reflection about (y = x): R2
Reflection about x-axis: R3
Reflection about y-axis: R3
Reflection about yz plane: R3
Orthogonal projection onto x-axis: R2
Orthogonal projection onto y-axis: R2
Orthogonal projection onto xy-plane: R3
Orthogonal projection onto xz-plane: R3
Orthogonal projection onto yz-plane: R3
Rotation operator on R2:
Counterclockwise rotation about the + x-axis through an angle theta
Counterclockwise rotation about the + y-axis through an angle theta
Counterclockwise rotation about the + z-axis through an angle theta