2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54863Self-dual 2-forms in D=2n dimensions are characterised by an eigenvalue criterion. The equivalence of various definitions of self-duality is proven. We show that the self-dual 2-forms determine a n^2-n+1 dimensional manifold S_{2n} and the dimension of the maximal linear subspaces of S_{2n}$ is equal to the Radon-Hurwitz number of linearly independent vector fields on the sphere S^{2n-1}. The relation between the maximal linear subspaces and the representations of Clifford algebras is noted. A general procedure based on this relation for the explicit construction of linearly self-dual 2-forms is given. The construction of the octonionic instanton solution in D=8 dimensions is discussed.14 pages, Latex (No figures) Paper presented to The 9th Max Born Symposium, Karpacz, Poland 25-27 September 1996High Energy Physics - Theorytext