Thread: L1-, L2-, Linfty-Norm Proofs - Please Help!

Show that ||x||1 < or = n||x||infinity and ||x||2 < or = sqrt(n)*||x||infinity for x exists in the set of all real numbers.

||x||2 is defined here: L2-Norm -- from Wolfram MathWorld
||x||1 is defined here: L1-Norm -- from Wolfram MathWorld
||x||infinity is defined here: L1-Norm -- from Wolfram MathWorld

Sorry about posting links, but I have no idea how to get all the symbols (like the summation symbol) to show up on the forums.

Anyway, thanks in advance for your help!

Originally Posted by theamazingjenny

Show that ||x||1 < or = n||x||infinity and ||x||2 < or = sqrt(n)*||x||infinity for x exists in the set of all real numbers.

||x||2 is defined here: L2-Norm -- from Wolfram MathWorld
||x||1 is defined here: L1-Norm -- from Wolfram MathWorld
||x||infinity is defined here: L1-Norm -- from Wolfram MathWorld

Sorry about posting links, but I have no idea how to get all the symbols (like the summation symbol) to show up on the forums.

Anyway, thanks in advance for your help!

What is x and what is n. By the look of this you intend x in R^n.

If so the first of these is trivial:

||x||_1 = sum_{i=1 to n} |x_i| < n max_{i=1 to n} |x_i| = n ||x||_{infty}

and the other is no more difficult

RonL