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squaremeplz
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Homework Statement
Does ||x||_inf = max | x_i | for 1 <= i <= n define a norm on R^(n)
Homework Equations
The Attempt at a Solution
ok, I thought I understood vector spaces but this problem is confusing the heck out of me.
A norm is a function that assigns a positive and finite length to all vectors in a vector space.
so ||x||_inf = sqrt(x1^2 + x2^2 + ... x_inf)
max |x_i| depends on n in R^n
Can someone give me like a simple example? i.e. n = 2
Then ||x||_inf = max (|x1|, |x2|)?
The maximum distance between all vectors would be equal to the distance from 0 to the greatest vector. rather, infinity would be considered bounded by the max vector?
Any help is greatly appreciated.
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