  The tropical Stiefel map associates to a tropical matrix A its tropical
Pluecker vector of maximal minors, and thus a tropical linear space L(A). We
call the L(A)s obtained in this way Stiefel tropical linear spaces. We prove
that they are dual to certain matroid subdivisions of polytopes of transversal
matroids, and we relate their combinatorics to a canonically associated
tropical hyperplane arrangement. We also explore a broad connection with the
secondary fan of the Newton polytope of the product of all maximal minors of a
matrix. In addition, we investigate the natural parametrization of L(A) arising
from the tropical linear map defined by A.
