Quaternionic vector space

Since quaternion algebra is division ring, then module over quaternion algebra is called vector space.

Because quaternion algebra is non-commutative, we distinguish left and right vector spaces.

In left vector space, linear composition of vectors

If quaternionic vector space has finite dimension

, then it is isomorphic to direct sum

copies of quaternion algebra

In such case we can use basis which has form In left quaternionic vector space

we use componentwise sum of vectors and product of vector over scalar

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