An inequality in matrices

Question

I am reading a paper. There is an upper bound for largest singular value of matrix $A$. Suppose its largest singular value is $d$ and $d\leq p$. Now we have a row vector $U$. It is said that in the paper $\|UA\|\leq \|U\|p$ but really I don't understand it. Could you please help me? Thanks in advance.

Answer 1

Assuming you are using $2$-norm, then it has the sub-multiplicative property.

Hence $$\|UA\| \le \|U\|\|A\|=\|U\|d \le \|U\|p$$