Geodesic
Monotone Additive Matrix Transformations
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 681-692

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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.
Keywords: matrix partial order, partially ordered set, Lewner order, Hartwig order, Drazin order, diamond order.
Mots-clés : monotone transformation 
@article{MZM_2007_81_5_a4,
     author = {A. \`E. Guterman},
     title = {Monotone {Additive} {Matrix} {Transformations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {681--692},
     publisher = {mathdoc},
     volume = {81},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a4/}
}
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A. È. Guterman. Monotone Additive Matrix Transformations. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 681-692. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a4/