Geodesic
Monotone matrix transformations defined
Sbornik. Mathematics, Tome 198 (2007) no. 1, pp. 1-16

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Bijective linear transformations of the matrix algebra over an arbitrary field that preserve simultaneous diagonalizability are characterized. This result is used for the characterization of bijective linear transformations monotone with respect to the $\stackrel{\sharp}$- and $\stackrel{\mathrm{cn}}$-orders. Bibliography: 28 titles. 
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I. I. Bogdanov; A. È. Guterman. Monotone matrix transformations defined. Sbornik. Mathematics, Tome 198 (2007) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/SM_2007_198_1_a0/