The trace of an Square Matrix *A* is defined by

(1) |

(2) | |||

(3) | |||

(4) |

(Lange 1987, p. 40). The trace is invariant under a Similarity Transformation

(5) |

(6) |

(7) |

where is the Kronecker Delta.

The trace of a product of square matrices is independent of the order of the multiplication since

(8) |

Therefore, the trace of the Commutator of and is given by

(9) |

(10) |

The value of the trace can be found using the fact that the matrix can always be transformed to a coordinate system where the
*z*-Axis lies along the axis of rotation. In the new coordinate system, the Matrix is

(11) |

(12) |

**References**

Lang, S. *Linear Algebra, 3rd ed.* New York: Springer-Verlag, pp. 40 and 64, 1987.

© 1996-9

1999-05-26