On faces generated by certain positive linear transformations
The paper deals with the cone of \(m\times n\) real matrices mapping a cone \(K_ 1\) in \({\mathbb{R}}^ n\) into a cone \(K_ 2\) in \({\mathbb{R}}^ m\). In the first part of the paper it is assumed that the matrices are of fixed rank and map the extreme rays of \(K_ 1\) into extreme rays of \(K_ 2\). Then under further assumptions an upper bound for the dimension of the face generated in the mapping cone of each of these matrices is given. In the second part of the paper it is shown that if a non-singular matrix maps the exposed rays of an indecomposable cone into itself then the matrix determines an exposed ray in the mapping cone.
scientific article; zbMATH DE number 4112783