# $l_2$ norm of the matrix

Suppose $$x \in \mathbb{R}^n$$ is a unit norm vector, and $$\mathbf{U} \in \mathbb{R}^{n \times n}$$ is a matrix such that $$\|\mathbf{U}\|_F = 1$$. We know that $$x^T \mathbf{U} x = 0$$.

From this fact, what can we say about $$\|U x x^T \|_2$$? Can we find an upper bound for that?