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Communications in Algebra Volume 33, 2005 - Issue 9
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Original Articles

Monotone Linear Transformations on Matrices Are Invertible

Anna A. Alieva Department of Mathematics and Mechanics, Faculty of Algebra, Moscow State University, Moscow, RussiaCorrespondence[email protected]
&
Alexander E. Guterman Department of Mathematics and Mechanics, Faculty of Algebra, Moscow State University, Moscow, Russia
Pages 3335-3352 | Received 01 Nov 2003, Accepted 01 Apr 2004, Published online: 05 Jan 5187
 
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ABSTRACT

We show that monotone linear transformations on matrices with respect to ¯<, , * <, < *, , , -partial orders are invertible and provide a complete characterization of such transformations.

Mathematics Subject Classification:

ACKNOWLEDGMENT

This work is partially supported by RFBR, grants YSF 03-55-1919 and NSH-1910.2003.01.

Notes

#Communicated by V. Artamonov.

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