spectral_norm_le_schatten_norm

For an exponent $q\ge 1$, the spectral (operator) norm of a real matrix $Y$ is at most its Schatten $q$-norm: $\lVert Y\rVert\le\lVert Y\rVert_{S_q}$. With singular values $\sigma_1\ge\sigma_2\ge\cdots$, $\sigma_1=(\sigma_1^q)^{1/q}\le(\sum_i\sigma_i^q)^{1/q}$ — the Schatten norms decrease to the operator norm as $q\to\infty$.