  The kinetic energy of a multi-particle system is described by the
one-particle kinetic energy density matrix $\tau(x, y)$. Alongside the
one-particle density matrix $\gamma(x, y)$, it is one of the key objects in the
quantum-mechanical approximation schemes. We prove the asymptotic formula
$\lambda_k \sim (Bk)^{-2}$, $B \ge 0$, as $k\to\infty$, for the eigenvalues
$\lambda_k$ of the self-adjoint operator $\boldsymbol{\sf T}\ge 0$ with kernel
$\tau(x, y)$.
