The Segre determinant is a polynomial which encodes the condition for points to lie
on a bilinear hypersurface in the product of projective spaces. We study Segre
determinants and compute them in various coordinate systems. We show that the
Segre determinant represents the Chow–Lam form of a generic torus orbit in the
Grassmannian. These Chow–Lam forms were introduced as a generalization of Chow
forms for projective varieties, and enjoy many similar properties. We also present
applications to algebraic vision and to Chow quotients of Grassmannians.
