Continuous monotone maps on matrices for orders induced by the group inverse
Mikhail A. Efimov, Alexander Emilevich Guterman · Journal of Mathematical Inequalities · 2016
We characterize continuous injective maps on the set of complex matrices which are monotone with respect to -order or cn -order. In particular, we prove that all such maps must be automatically R -linear and surjective. We also present several examples of monotone maps showing that our assumptions are indispensable.