- 57

- 0

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