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Homescalar factor transfer rules

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# scalar factor transfer rules

The different kinds of products between two Euclidean vectors may contain an additional scalar as factor in either vector factor $\vec{u}$, $\vec{v}$. Then such a scalar $r$ can be transferred from a vector to the other vector and to the whole product. This is true for scalar product,

$\vec{u}\!\cdot\!(r\vec{v})=(r\vec{u})\!\cdot\!\vec{v}=r(\vec{u}\!\cdot\!\vec{v% }),$ |

for vector product,

$\vec{u}\!\times\!(r\vec{v})=(r\vec{u})\!\times\!\vec{v}=r(\vec{u}\!\times\!% \vec{v}),$ |

and also for dyad product,

$\vec{u}(r\vec{v})=(r\vec{u})\vec{v}=r(\vec{u}\vec{v}).$ |

Keywords:

scalar multiplication

Synonym:

transfer rules of scalar factor

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Topic

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Reference

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## Mathematics Subject Classification

15A72*no label found*

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