Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

See here. What is the usual definition of $||A||$ for an $n\times n$ matrix $A$?


share|cite|improve this question
The proof of the inverse function theorem uses the operator norm. – scineram Apr 9 '11 at 8:46
up vote 1 down vote accepted

In finite dimensional vector space all norms are equivalent, that's why in the given link, the norm is not specified. If you want to have a particular norm just think of matrix $A$ as an $n^2$ tuple and use the standard norm on $\mathbb{R}^{n^2}$.

share|cite|improve this answer
There are other norms for $n\times n$ matrices. – Alex Becker Apr 9 '11 at 2:18
@Alex: Yes, but as user0977 was saying, they're all equivalent. – Jesse Madnick Apr 9 '11 at 2:51
@Jesse: Sorry, for some reason I was thinking that the induced and componentwise norms were nonequivalent. – Alex Becker Apr 9 '11 at 3:04

The usual norm is the "operator norm" induced from the norms on the vector spaces that A maps from and to, defined as $\sup\{||Ax||:||x||=1\}$; in your case, it's probably the square root of the largest eigenvalue of A*A, where A* is the conjugate transpose of A:

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.