Let x be a vector. How do you show that [tex]\left\| x^{*} \right\| _{p} = \left\| x \right\| _{q}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

where [tex]\frac{1}{p} + \frac{1}{q} = 1[/tex]

By using this definition of [tex]\left\| x^{*} \right\| _{p} = max_{ \left\| y \right\| _{p} =1} \left\| x^{*} y \right\| _{p} [/tex]

and Holder's inequality, I am able to prove that

[tex]\left\| x^{*} \right\| _{p} \leq \left\| x \right\| _{q}[/tex]

But how do you show the other side of the inequality?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: How do you show the other side of the inequality?

**Physics Forums | Science Articles, Homework Help, Discussion**