  We observe that linear relations among Chern-Mather classes of projective
varieties are preserved by projective duality. We deduce the existence of an
explicit involution on a part of the Chow group of projective space, encoding
the effect of duality on Chern-Mather classes. Applications include Pl\"ucker
formulae, constraints on self-dual varieties, generalizations to singular
varieties of classical formulas for the degree of the dual and the dual defect,
formulas for the Euclidean distance degree, and computations of Chern-Mather
classes and local Euler obstructions for cones.
