Abstract
We investigate additive transformations on the space of real or complex matrices that are monotone with respect to any admissible partial order relation. A complete characterization of these transformations is obtained. In the real case, we show that such transformations are linear and that all nonzero monotone transformations are bijective. As a corollary, we characterize all additive transformations that are monotone with respect to certain classical matrix order relations, in particular, with respect to the Drazin order, left and right*-orders, and the diamond order.
| Original language | English |
|---|---|
| Pages (from-to) | 609-619 |
| Number of pages | 11 |
| Journal | Mathematical Notes |
| Volume | 81 |
| Issue number | 5-6 |
| DOIs | |
| State | Published - Jun 2007 |
| Externally published | Yes |
Bibliographical note
Funding Information:The author is grateful to A. A. Alieva and A. V. Mikhalev for interesting discussions. This work was supported in part by the Russian Foundation for Basic Research (grant no. 05-01-01048) and by grant no. MK-1417.2005.1.
Funding
The author is grateful to A. A. Alieva and A. V. Mikhalev for interesting discussions. This work was supported in part by the Russian Foundation for Basic Research (grant no. 05-01-01048) and by grant no. MK-1417.2005.1.
| Funders | Funder number |
|---|---|
| Russian Foundation for Basic Research | 05-01-01048 |
Keywords
- Diamond order
- Drazin order
- Hartwig order
- Lewner order
- Matrix partial order
- Monotone transformation
- Partially ordered set