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

In, unitary space seems to be Hilbert space. But in, "finite dimensional" is required. My question is, which definition of unitary space is commonly used?

share|cite|improve this question
up vote 6 down vote accepted is wrong. Unitary space is an archaic name for complex inner product space.

share|cite|improve this answer
But not necessarily complete, so it's also definitely not the same as complex Hilbert space. – tomasz Aug 13 '12 at 13:55
You mean there's something wrong on the internet? Noooooooooo! – Pete L. Clark Aug 13 '12 at 13:59
Seriously, as kahen says, the term "unitary space" is not itself commonly used nowadays, so far as I'm aware. Instead people (especially analysts) will speak of complex inner product spaces while others (especially algebraists) will speak of Hermitian spaces. – Pete L. Clark Aug 13 '12 at 14:01
@PeteL.Clark: To be fair, I remember the term used in my first year linear algebra course (it did focus mostly on finite-dimensional spaces, and I can't recall if the definition used there assumed finite dimension, but I doubt it did). Also, another term I've heard is pre-Hilbert space. – tomasz Aug 13 '12 at 14:05
Just saying pre-Hilbert space doesn't specify whether it's complex or not though. – kahen Aug 13 '12 at 14:39

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.