Resumo:
We present our recent results on the characterization of monotone
transformations on matrix spaces with respect to various matrix partial
orders, in particular, the orderings defined in terms of generalized
inverses. Among the other results we show that surjective monotone
additive transformations on matrices with respect to various matrix
partial orders are invertible and provide a complete characterization of
such transformations. It turns out that the thinner the matrix partial
order under consideration is the smaller is the class of corresponding
monotone transformations. |