Im wondering whether this expression holds for all matrices
$$ ||diag(A(X-Y))|| \le \lambda_{max}(diag(A))||diag(X-Y)|| $$
where diag is selecting only the diagonal entries of the matrix, and $\lambda_{max}$ could be the maximum eigenvalue OR the maximum singular value
and would the following expression be wrong?
$$ ||diag(A(X-Y))|| \le \lambda_{max}(A)||diag(X-Y)|| $$
^If this expression is not wrong, then I am guessing it would just give us a weaker (less tight) bound in comparison to the first expression right?
Thank you for taking the time, I really appreciate any help I could get!