# Matrix norms

1. Oct 18, 2008

### dirk_mec1

Last edited by a moderator: May 3, 2017
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
$$||Ax||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}$$

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