In left-handed coordinate system, positive angle is clockwise direction. In right-handed coordinate system, positive angle is anti-clockwise direction.
I spent many hours to find out how to convert rotation matrices of left-handed coordinate system. The solution is to replace the angle with
The rotation matrices about three axis in left-handed coordinate system.
The rotation matrix about arbitrary axis
To get in right-handed coordinate system, replace the angle with negative . Then apply the following rules.
3D Math Primer for Graphics and Game Development 2ed, Fletcher Dunn, Ian Parberry
Mathematics for 3D Game Programming and Computer Graphics 3ed, Eric Lengyel