# Matrix norms

1. Oct 18, 2008

### dirk_mec1

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
I think it is crucial that [itex] ||x||_1=1[/tex] but I don't see how I can use that info. Can someone help me?

2. Oct 18, 2008

### Pere Callahan

Try to show
$$||A||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}$$
and
$$||A||_1 \leq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}$$
separately. Can you prover either of these statements?

Hint: For the first one it is enough to find an x with norm one such that
$$||Ax||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}$$