Question
Find a matrix $A$ such that $\left\|A^2\right\|_{\infty} \neq\|A\|_{\infty}^2$.
Step 1
The infinity norm of a matrix $A$, denoted $\|A\|_{\infty}$, is defined as the maximum absolute row sum of $A$. That is, $\|A\|_{\infty} = \max_{1 \leq i \leq n} \sum_{j=1}^n |a_{ij}|$, where $a_{ij}$ are the elements of the matrix $A$. Show more…
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