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> would not support quaternions but would completely satisfy the given constraints. |
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. |
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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) |
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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