Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Reading the wiki article I get confused about matrix norms. My question, is it true that $$\lVert Mx \rVert \leq C(\sup_{ij}{M_{ij}}) \lVert x \rVert$$ where $M$ is a matrix and $x$ is a vector and $C$ is some constant? What does $C$ depend on?

According to wiki, $\lVert Mx \rVert \leq \rho(M) \lVert x \rVert$ holds where $\rho$ denotes the spectral radius.

But aren't all finite dimensional norms equivalent, so I can write my first formula? thank you.

share|cite|improve this question
Yes, you can (the exact value of $C$ will depend on the particular choice of norm in the space and the matrix size). ---According to wiki, $\|Mx\|\le\rho(M)\|x\|$ holds where $\rho$ denotes the spectral radius--- This is nonsense as written. Where have you seen it? – fedja Nov 15 '12 at 19:56
@fedja Thanks, good to know. so I can use the standard Euclidean norms. I thought I saw the spectral radius thing in wiki, but I guess not, but I found (…) where Fabian suggested something like it.. – maximumtag Nov 15 '12 at 21:10

Your Answer


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

Browse other questions tagged or ask your own question.