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Subordinate matrix norm
I have a question in my homework for Numerical Linear Algebra, which is as follows:
Show that the norm $\|A\| = \max \limits_{i, j} |a_{i,j}|$ on the space of $n \times n$ real matrices is not induced by any vector norm.
Can anyone help me solve the problem?
This problem was on the homework given to us on our first class, and I've no idea how to solve.
Thanks.