"Let [tex]Mat_n[/tex] denote the space of [tex]n\times n[/tex] matrices. For [tex]A\in Mat_n[/tex], define the norms [tex]||A||_1[/tex] as follows:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]||A||_1=\sup_{0\neq x\in\mathbb{R}^n}\frac{||Ax||}{||x||}[/tex],

where ||x|| is the usual Euclidean norm.

Prove that this norm is really a norm (triangle ineq, etc)"

I don't know how to even prove that the supremum exists.

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

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: Matrix Norm

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