# Homework Help: Norm inequality, find coefficients

1. Sep 5, 2016

### lep11

• Member warned that homework posts must include an effort
1. The problem statement, all variables and given/known data
Find coefficients a,b>0 such that a||x||≤||x||≤b||x||.

2. Relevant equations

3. The attempt at a solution
No idea how to get started. Help will be appreciated.

Last edited by a moderator: Sep 5, 2016
2. Sep 5, 2016

### Math_QED

You must have tried something? You must have thought something? Share it with us because you are required to show some effort.

3. Sep 5, 2016

### lep11

I have no idea how to find the coefficients...and I am not expecting you to do my homework.

it has something to do with equivalence of norms?

Last edited: Sep 5, 2016
4. Sep 5, 2016

### pasmith

How is $\|x\|$ defined?
How is $\|x\|_{\infty}$ defined?
What is the dimension of the space on which these norms are defined?

5. Sep 5, 2016

### Ray Vickson

Yes, that is exactly what the problem is about---showing how to prove norm equivalence.

6. Sep 5, 2016

### micromass

What space is $x$ a member of? How are the norms defined?

7. Sep 5, 2016

### Staff: Mentor

@lep11, definitions of these two norms would have been useful in the (empty) Relevant equations section.

8. Sep 6, 2016

### lep11

$\|x\|:=(\sum_{i=1}^{n} x_i^2)^½$
$\|x\|_{\infty}$:=max{|x1|,...,|xn|}

x∈Rn, so dimension of the space is n.

9. Sep 6, 2016

### Ray Vickson

Why don't you look first at the case of $n=2$, where you can easily draw pictures and make $(x_1,x_2)$-diagrams to help you focus your thinking?

10. Sep 6, 2016

### Staff: Mentor

At 9 posts into this thread, the OP still has not shown an attempt -- thread closed.

@lep11, you may start another thread on this question, but you MUST show some effort or there will be consequences.