The matrix representing a general rotation in three dimensions is

This is a complicated matrix but for rotations about one of the coordinate axes it simplifies considerably.

A rotation about the- axis fixes We need a 1 in the top left hand corner and zero's in the first row and column. Taketo give.

A rotation about the- axis fixesWe need a 1 in the middle and zeros in the second column and row. Taketo give

A rotation about the– axis fixesWe need a 1 in the bottom right hand corner and zeros in the third column and row. Taketo give

The anglesare called Euler angles. The general rotation matrix can be obtained by multiplying the three rotation matrices together.