Rotation matrix is a kind of matrix. When it is multiplied with a vector, it can change the direction of the vector without changing its size and keep its chirality. The rotation matrix does not contain point inversion, which can change handedness, that is, change the right-handed coordinate system into the left-handed coordinate system or vice versa.

All rotations are added and inverted to form a set of orthogonal matrices. Rotation can be divided into active rotation and passive rotation. Active rotation means that the pointing quantity rotates counterclockwise around the rotation axis. Passive rotation is the counterclockwise rotation of the coordinate axis itself, which is equivalent to the reverse operation of active rotation.

Mathematically, the principle of rotation matrix involves a combination design: covering design. Covering design, filling design, Steiner system and t- design are all combinatorial optimization problems in discrete mathematics. They solve the problem of how to combine elements in a collection to achieve specific requirements.

A teacher is going to arrange for fifteen girls in the class to take a walk like this: three girls in a group and five groups. Can you arrange a walk every day for a week, so that every two girls can walk together just once a week? Kirkman put forward this problem in 1847, but the existence of the general Kirkman problem will take 100 years to be completely solved.