CONICET | Buscador de Institutos y Recursos Humanos

We study certain pairs of subspaces V and W of C^n we callsupports that consist of eigenspaces of the eigenvalues plus or minus the norm of a minimal hermitian matrix M (that is, the norm of M is less or equal tnat the norm of M + D for all real diagonals D).For any pair of orthogonal subspaces we define a non negative invariant called the adequacy to measure how close they are to form a support and to detect one. This function is the minimum of another map F defined in a product of spheres of hermitian matrices. We study the gradient, Hessian and critical points of F in order to approximate the adequacyh. These results allow us to prove that the set of supports has interior points in the space of flag manifolds.