group inverse (original) (raw)
Let A be an n×n matrix over ℝ. A group inverse for A is an n×n matrixX such that
| AXA | =A | (1) |
|---|---|---|
| XAX | =X | (2) |
| AX | =XA. | (3) |
Such a matrix, when it exists, is unique and is denoted by A#. 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 |