= Zero-diagonal Jacobi Lax pair for the finite Volterra lattice
{c}
Let $L$ be the symmetric zero-diagonal <Jacobi matrix> with $L_{j,j+1}=L_{j+1,j}=a_j$, and let the <skew-symmetric matrix> $B$ have
$$
B_{j,j+2}=-B_{j+2,j}=a_ja_{j+1}.
$$
Then $\dot L=[B,L]$ is equivalent to the <Finite Volterra lattice>. The corresponding similarity flow makes the eigenvalues of $L$, the coefficients of its <characteristic polynomial>, and its <trace invariants of a Lax equation>[trace invariants] first integrals.
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