Talk:Geometric algebra: Difference between revisions
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in a fashion which does not support quaternion multiplication. For example, an algebra where <math>\forall \mathbf{x}\in\mathcal{V},\forall \mathbf{y}\in\mathcal{V},\,\mathbf{xy}\in\R</math> and <math>\forall \mathbf{x}\in\mathcal{V},\forall \mathbf{y}\in\mathcal{R},\,\mathbf{xy}\in\R</math> and <math>\forall \mathbf{x}\in\mathcal{R},\forall \mathbf{y}\in\mathcal{V},\,\mathbf{xy}\in\R</math> would not support quaternions but would completely satisfy the given constraints.
And, in fact, there are arbitrarily many complex rules one could apply to achieve quaternion multiplication and still satisfy those constraints. This means that the specification is incomplete. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 22:49, 17 October 2015 (UTC)
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