Abstract
We study certain pairs of subspaces V and W of Cn 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.
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