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Possible Duplicate:
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.

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    Thanks a lot. I had no idea that stackexchange accepts Tex format.2012-01-10
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    What do you mean exactly by "induced by vector norm"? That it is of the form $max_{|x|=1}|Ax|$?2012-01-10
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    If you mean what yohBS guesses, try checking submultiplicativity. That is, $\|AB\|\leq \|A\|\|B\|$ is not always satisfied, and there are simple $2$-by-$2$ counterexamples. (You need $n>1$ of course.) I will remove my downvote if the question is clarified.2012-01-10
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    (Ah, Jonas added the hint!) I _think_, if I recall the trick correctly, that this is most easily shown by using some theory, and not arguing using elementary considerations. So it would really help to know: what's you background. What course is this from? What sort of techniques do you know? What else have you been doing recently in this course? etc. etc.2012-01-10
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    This question seems to be a duplicate of [this earlier post](http://math.stackexchange.com/q/67278/13425). Anyway, we seem to be awaiting some clarification from the OP, so I am not voting to close now.2012-01-10
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    @Srivatsan: Thanks for the find. I will vote to close. We can always reopen if it is closed by mistake before it is clarified. In the meantime, the question is already being answered as though it is a duplicate of (part of) that question.2012-01-10
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    This question seems to be the duplicate of the question referred to by @Srivatsan. I will go ahead and delete the question. Thanks.2012-01-11
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    @rookieRailer Please do not delete the question, just let it be. (In any case, since there is already an answer with upvotes, I think you will not be allowed to delete it now.)2012-01-11

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