FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 4, PAGES 53-66

## Linear matrix transformations that are monotone with respect to the $\overset \left\{\sharp \right\}\left\{\leq \right\}$- or $\overset \left\{\textrm \left\{cn\right\}\right\}\left\{\leq \right\}$-order

M. A. Efimov

Abstract

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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 $\overset \left\{\sharp \right\}\left\{\leq \right\}$- or $\overset \left\{\mathrm \left\{cn\right\}\right\}\left\{\leq \right\}$-order.

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