- #1
Dragonfall
- 1,030
- 4
"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:
[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.
[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.