Abstract
The equations for the (finite, nonperiodic) Toda lattice can, as is well known, be written in Lax form, $$\dot X(t) = [X(t),\Pi X(t)]$$ Here X is a symmetric tridiagonal matrix and Π is the projection onto the skew-symmetric summand in the decomposition of X into skew-symmetric plus upper triangular. The eigenvalues of X are constants of motion of (1), and the Toda lattice turns out to be a completely integrable Hamiltonian system.
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