schatten_even_pow_le_trace_dilation_even_pow

Schatten even-power moment ≤ dilation trace moment. For a real rectangular matrix $X$ and $n \ge 1$, the $2n$-th power of the Schatten-$2n$ norm is bounded by the trace of the $2n$-th power of the Hermitian dilation $\mathcal{H} = \begin{pmatrix}0 & X\\ X^\top & 0\end{pmatrix}$: $\|X\|_{S_{2n}}^{2n} \le \operatorname{tr}(\mathcal{H}^{2n})$. Proof (reduction): $\|X\|_{S_{2n}}^{2n} = \operatorname{tr}((XX^\top)^n)$ (Schatten even-power = row-Gram trace), and $\operatorname{tr}(\mathcal{H}^{2n}) = \operatorname{tr}((XX^\top)^n) + \operatorname{tr}((X^\top X)^n)$ (dilation trace identity), with $\operatorname{tr}((X^\top X)^n) \ge 0$ since $X^\top X$ is positive semidefinite. This routes the rectangular Schatten moment onto the symmetric Hermitian trace-moment engine.