Geodesic
Linear matrix transformations that are monotone with respect to the $\overset\sharp\leq$- or $\overset{\mathrm{cn}}\leq$-order
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 4, pp. 53-66

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We characterize linear transformations on the matrix algebra over an arbitrary field with characteristic not equal to 2 that are monotone with respect to the $\overset\sharp\leq$- or $\overset{\mathrm{cn}}\leq$-order. 
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     author = {M. A. Efimov},
     title = {Linear matrix transformations that are monotone with respect to the $\overset\sharp\leq$- or $\overset{\mathrm{cn}}\leq$-order},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {53--66},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_4_a2/}
}
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M. A. Efimov. Linear matrix transformations that are monotone with respect to the $\overset\sharp\leq$- or $\overset{\mathrm{cn}}\leq$-order. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 4, pp. 53-66. http://geodesic.mathdoc.fr/item/FPM_2007_13_4_a2/