Supports for minimal hermitian matrices.

We study certain pairs of subspaces V and W of C n we call supports that consist of eigenspaces of the eigenvalues ± ‖ M ‖ of a minimal hermitian matrix M (‖ M ‖ ≤ ‖ M + D ‖ for all real diagonals D). For any pair of orthogonal subspaces we define a non negative invariant δ called the adequacy to measure how close they are to form a support and to detect one. This function δ 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 δ. These results allow us to prove that the set of supports has interior points in the space of flag manifolds. [ABSTRACT FROM AUTHOR]