The dot product can be defined by

(1) |

(2) | |||

(3) |

it follows that (1) yields

(4) |

So, in general,

(5) |

(6) |

(7) |

(8) |

(9) |

(10) |

where Einstein Summation has been used.

The dot product is also defined for Tensors and by

(11) |

**References**

Arfken, G. ``Scalar or Dot Product.'' §1.3 in *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL:
Academic Press, pp. 13-18, 1985.

© 1996-9

1999-05-24