Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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Problem 3. (Operator Norms.) In Mod3-L2 we saw the concept of an operator norm:
|| Ax ||p
|| A||,
= max ||Ax ||p.
||2||=1
= max
In lecture we saw that
m
||4||1
max ||Ax1
||x||1=1
max
j=1,...,n
i=1
> Jaij i.e., the max column sum
where ||x||1 =E; ai|. Show that this equality holds. That is, show that ||A||1 is in fact the max
column sum.
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Transcribed Image Text:Problem 3. (Operator Norms.) In Mod3-L2 we saw the concept of an operator norm: || Ax ||p || A||, = max ||Ax ||p. ||2||=1 = max In lecture we saw that m ||4||1 max ||Ax1 ||x||1=1 max j=1,...,n i=1 > Jaij i.e., the max column sum where ||x||1 =E; ai|. Show that this equality holds. That is, show that ||A||1 is in fact the max column sum.
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