Quaternionic vector space: Difference between revisions

Revision as of 08:33, 18 December 2015

Revision as of 21:11, 19 August 2021

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In [[mathematics]], a '''left''' (or '''right''') '''quaternionic vector space''' is a left (or right) '''H'''-[[module (mathematics)|module]] where '''H''' denotesis the (non-commutative) [[ring (mathematics)|noncommutativedivision ring]] of the [[quaternion]]s.

The space '''H'''^''n'' of ''n''-tuples of quaternions is both a left and right '''H'''-module using the componentwise left and right multiplication:

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for quaternions ''q'' and ''q''₁, ''q''₂, ... ''q''_''n''.

Since '''H''' is a [[division algebra]], every [[Finitely generated module|finitely generated]] (left or right) '''H'''-module has a [[basis (linear algebra)|basis]], and hence is [[isomorphic]] to '''H'''^''n'' for some ''n''.

==See also==