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Matrix norms

timmy

New member
May 5, 2012
1
Hi all, I think I have part of the answer to my question but I need some help if you would be so kind.

Q: a)Compute the condition number of the following matrix using matrix norms ||A||_1 and ||A||_infinity.
[a 1]
[1 1]

And also: What values of a give a large condition number?

So ||A||_1= either 2 or (|a|+1), whichever is bigger. So it would be written as max(2,|a|+1).
And ||A||_infinity is the same as ||A||_1.

How do I bring this together to get the answer I need?


b) Is the following expression a valid norm for x in R^n?
max{|x_2|,|x_3|,|x_4|,...,|x_n|}

Got nothing for this one.

Thanks for any help guys!

Timmy
 

girdav

Member
Feb 1, 2012
96
For the first question, you have to compute the norm of $A^{-1}$, and for the second question, $x_1$ may be not equal to $0$, even if the "norm" of $x$ is $0$.
 
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