The computation of isotropic vectors

We describe algorithms to compute isotropic vectors for matrices with real or complex entries. These are unit vectors b satisfying b ^* Ab = 0. For real matrices the algorithm uses only the eigenvectors of the symmetric part corresponding to the extreme eigenvalues. For complex matrices, we first use the eigenvalues and eigenvectors of the Hermitian matrix K = (A − A ^*)/2i. This works in many cases. In case of failure we use the Hermitian part H or a combination of eigenvectors of H and K. We give some numerical experiments comparing our algorithms with those proposed by R. Carden and C. Chorianopoulos, P. Psarrakos and F. Uhlig.