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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
##### Keywords:
linear transformations; matrix algebra; monotone
Full Text:
##### References:
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