Is there an accepted term for the following property?

Let $A$ be a real matrix such that all entries of the eigenvector corresponding to the least eigenvalue have the same sign.

NOTES: (1) The case of multiple eigenvalues might be messy, I don't mind disregarding it at this stage. (2) irreducible Z-matrices, negatives of eventually positive matrices, and inverse-positive matrices all have this property - what I'm looking for is a more general name.

If no standard name comes up, what do you think of the name "minpositive"?