Bojan Tunguz tunguz [snail] g.a.l.com Is there a way that a rank-four tensor can be brought to a bi-diagonal form using some unitary group transformations? If not an arbitrary four-tensor, is there a class of such tensors that can be brought to this form? Predrag: what is 'bi-diagonal?' Diagonal in first index pair, and diagonal in the second index pair? Not a chance, unless you have some more specific properties, corresponding to hermiticity or symmetry for a 2-index tensor (AKA matrix).