Combinatorial types of tropical eigenvectors
Bernd Sturmfels, Ngoc Mai Tran · Bulletin of the London Mathematical Society · 2012
The map which takes a square matrix to its tropical eigenvalue–eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.