FPM 2007, vol. 13, no. 4, pp. 53-66

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

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

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