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Adding local short description: "Module over the algebra of quaternions.", overriding Wikidata description "module over the algebra of quaternions" |
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{{Short description|Module over the algebra of quaternions.}}
In [[noncommutative algebra]], a branch of [[mathematics]], a '''quaternionic vector space''' is a [[Module (mathematics)|module]] over the [[Quaternion|quaternions]]. Since the quaternion algebra is [[division ring]], these modules are referred to as "vector spaces". However, the quaternion algebra is [[Noncommutative ring|noncommutative]] so we must distinguish left and right vector spaces. In left vector spaces, linear compositions of vectors <math> v</math> and <math> w</math> have the form <math> av+bw</math> where <math> a</math>, <math> b\in H</math>. In right vector spaces, linear compositions of vectors <math> v</math> and <math> w</math> have the form <math> va+wb</math>.
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