# group inverse

Let $A$ be an $n\times n$ matrix over $\mathbb{R}$.
A *group inverse* for $A$ is an $n\times n$ matrix
$X$ such that

$AXA$ | $=A$ | (1) | ||

$XAX$ | $=X$ | (2) | ||

$AX$ | $=XA.$ | (3) |

Such a matrix, when it exists, is unique and is denoted by ${A}^{\mathrm{\#}}$. A group inverse is a special case of a Drazin inverse.

Title | group inverse |
---|---|

Canonical name | GroupInverse |

Date of creation | 2013-03-22 17:01:17 |

Last modified on | 2013-03-22 17:01:17 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 5 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 15A09 |