Given an Matrix
, the Moore-Penrose generalized Matrix Inverse is a unique
Matrix
which satisfies

(1) | |||

(2) | |||

(3) | |||

(4) |

It is also true that

(5) |

(6) |

If the inverse of
exists, then

(7) |

(8) |

(9) |

**References**

Ben-Israel, A. and Greville, T. N. E. *Generalized Inverses: Theory and Applications.* New York: Wiley, 1977.

Lawson, C. and Hanson, R. *Solving Least Squares Problems.* Englewood Cliffs, NJ: Prentice-Hall, 1974.

Penrose, R. ``A Generalized Inverse for Matrices.'' *Proc. Cambridge Phil. Soc.* **51**, 406-413, 1955.

© 1996-9

1999-05-26