On solving an isospectral flow

In this paper we expand the solution of the matrix ordinary differential system, originally due to Bloch and Iserles, of the form X′=[N,X2],t≥0,X(0)=X0∈Sym(n),N∈so(n), where Sym(n)Sym(n) denotes the space of real n×nn×n symmetric matrices and so(n)so(n) denotes the Lie algebra of real n×nn×n skew-symmetric matrices. The flow is solved using explicit Magnus expansion, which respects the isospectrality of the system. We represent the terms of expansion as binary rooted trees and deduce an explicit formalism to construct the trees recursively.