The spectral norm (induced 2-norm) of a matrix is $\|A\|_2 = \max_{\|x\|_2 = 1} \|Ax\|_2$. For any matrix, the spectral norm equals the largest singular value of $A$. This is different from the Frobenius norm $\|A\|_F = \sqrt{\sum_{i,j} a_{ij}^2}$. For the matrix $A = \begin{pmatrix} 1 & 1 \\ 0 & 0 \end{pmatrix}$, which inequality is correct?