Asymptotic Analysis of Toda Lattice on Diagonalizable Matrices

is a skew-symmetric matrix. Equation (1.1) is known as the Toda lattice. Among many of its interesting properties which have been studied [2-4, 7, 111, probably the most important features are the isospectral property-starting with any initial value L(0) = Lo, the solution flow L(f) of (1.1) has the same spectrum for all r, and the global asymptotic convergence property-the solution flow L(t), while preserving the tridiagonal form for all t, converges to a diagonal matrix. Recently the significance of this dynamical system was further underscored by the discovery