Let $X\in\mathbb{R}^{n\times d}$ be a random matrix, and $\{m_k\}_{k=1}^K, m_k \in \mathbb{R}^{d}$ be a fixed set of matrices. I was wondering, what is the expectation (or upper bound of the expectation) of
$\mathbb{E}\max_{k}\{||Xm_k||_2^2\}$
Any comment or hint will be appreciated!