Question on quaternions (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

I read in some text the following:
Quaternion algebra becomes a normed vector(linear) space with appropriate norm ...(blah blah)... Also since every element has a multiplicative inverse it is a field.

Now, what I find confusing is that according to above a mathematical object called quaternion is not only an algebra but with the norm normed linear space and furthermore a field?? In other words, all these notions of algebra+nvs+field etc should be regarded as some kind of characterisation of an object of our interest in this case quaternion? or further rephrasing this, different ways of looking at an object quaternion?

I would appreciate your comment


Staff Emeritus
Science Advisor
Insights Author
Quaternion multiplication is not commutative. The quaternions form a division ring, not a field.


Staff Emeritus
Science Advisor
Gold Member
Ah, I think this has what you want to know. (and maybe the results at the bottom of this)
Last edited:

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving