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

Just finished a course in linear algebra, where the norm of a vector essentially was described as the length of the vector. In calculus, we just started talking about the definite integral of a function, where the norm of a partition came up, being defined as the max size of a subinterval given a set of subintervals.

Are these two uses of norm related, and if so how?

share|cite|improve this question
up vote 1 down vote accepted

The max size of the absolute value of a finite list of numbers is the infinity-norm of that list. This is an example of a p-norm. For $p=2$ you get the Euclidean norm that you're familiar with.

share|cite|improve this answer

In addition to what @vadim said, it is just used because of norm-like properties such as $$ \|\mathcal{P}\| > 0 $$ for any partition $\mathcal{P}$, and $$ \|\mathcal{P}_1\cup\mathcal{P}_2\| \leq \max\{\|\mathcal{P}_1\|, \|\mathcal{P}_2\|\} $$ In other words, it is some measure of the size of a partition that behaves well with respect to the algebraic operations that one can perform on partitions.

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.