# How to convert a right handed rotation matrix into a left handed one?

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Nora Hora on 25 Jan 2017
Commented: Niels on 25 Jan 2017
Previsouly I used this(page 7): http://answers.unity3d.com/storage/temp/12048-lefthandedtorighthanded.pdf to transform my rotational matrix into a right handed one. Now I would like to make the opposite with a right handed one into left. Is there any suggestion? See my left to right conversion which is based on this paper.
[RH_R]=left_to_right(R_cw, alpha, beta, gamma)
%%left-handed rotation angles
theta_x = gamma;
theta_y = beta;
theta_z = alpha;
%%left-handed coordinate rotation matrices
R_cw_X = [1 0 0; 0 cos(theta_x) -sin(theta_x); 0 sin(theta_x) cos(theta_x)];
R_cw_Y = [cos(theta_y) 0 sin(theta_y); 0 1 0; -sin(theta_y) 0 cos(theta_y)];
R_cw_Z = [cos(theta_z) -sin(theta_z) 0; sin(theta_z) cos(theta_z) 0; 0 0 1];
%%left-handed composite rotation
LH_R= R_cw_Z * R_cw_Y * R_cw_X;
%%right-handed composite rotation
RH_R=LH_R;
RH_R(1,3) = -RH_R(1,3);
RH_R(2,3) = -RH_R(2,3);
RH_R(3,1) = -RH_R(3,1);
RH_R(3,2) = -RH_R(3,2);

Niels on 25 Jan 2017
to change the direction of rotation it is enough to transpose the rotation matrix
if matrix A rotates clockwise then
A' rotates anticlockwise
Niels on 25 Jan 2017
same for the opposite case.
you could also just use the negativ angle (same effect) -> replace theta with -theta)