Setup: Given that I have a random square matrix $X$ where each entry is generated independently and identically. Denote $\|X\|_{\text{op}}$ to be the operator norm of the square matrix.
Question: Given that the distribution of the entries of $X$ satisfy some assumptions, we have the result that $\|X\|_{\text{op}}<C$ almost surely for some constant $C$ -- this is a known result that we can take for granted. If I were to generate another rectangular matrix $Y$ in the same manner, i.e., each entry of $Y$ is generated independently and identically with the same distribution as the entries of $X$, does the previous result (i.e., $\|X\|_{\text{op}}<C$ almost surely) imply that $\|Y\|_{\text{op}}<C$ almost surely for some constant $C$? Thanks.
Remark: I have avoided stating the result in full as it makes the question unnecessarily complex. But for completeness the result that I am looking at is from this paper, Theorem 2.7 and Eq. (2.4).