I am considering two $M\times N$ matrices $\mathbf{A}$ and $\mathbf{B}$ and am computing $l_1$ distance between them
\begin{equation} \|\mathbf{A}-\mathbf{B}\|_1=\sum_{m,n}|a_{mn}-b_{mn}| \end{equation}
My question is: if $\|\mathbf{A}-\mathbf{B}\|_1$ turns out to be a small (but not like $\epsilon$ small) then can we say that $\Sigma_{\mathbf{A}}\approx\Sigma_{\mathbf{B}}$ where $\Sigma$ are the singular values of a matrix i-1 $svd(\mathbf{A})=\mathbf{U}\Sigma\mathbf{V}^T$