Invariant subspaces of two Hermitian structures on a Euclidean space Original Research Article

Let (left angle bracket,right-pointing angle bracket,J1) and (left angle bracket,right-pointing angle bracket,J2) denote two Hermitian structures on a 2n-dimensional Euclidean space (V,left angle bracket,right-pointing angle bracket). If n is even and J1,J2 have opposite orientations, then there exist non-zero vectors v,wset membership, variantV such that J1(v)=J2(v) and J1(w)=−J2(w). If n is odd and J1,J2 have the same orientation (resp. opposite orientation), then there exists a non-zero vector vset membership, variantV such that J1(v)=J2(v) (resp. J1(v)=−J2(v)).