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Linear matrix transformations that are monotone with respect to the \(\leq^\sharp\)-or \(\leq^{\mathrm{cn}}\)-order. (English. Russian original) Zbl 1157.15303
J. Math. Sci., New York 155, No. 6, 830-838 (2008); translation from Fundam. Prikl. Mat. 13, No. 4, 53-66 (2007).
Summary: 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 \(\leq^\sharp\)-or \(\leq^{\text{cn}}\)-order.
MSC:
15A04 Linear transformations, semilinear transformations
15A30 Algebraic systems of matrices
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