PlanetMath: scalar factor transfer rules

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scalar factor transfer rules

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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 can be transferred from a vector to the other vector and to the whole product. This is true for scalar product,

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

for vector product,

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

and also for dyad product,

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

"scalar factor transfer rules" is owned by pahio.

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Other names:

transfer rules of scalar factor

Keywords:

scalar multiplication

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Cross-references: dyad product, vector product, scalar product, vector, factor, scalar, Euclidean vectors, products
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This is version 2 of scalar factor transfer rules, born on 2005-08-04, modified 2005-08-04.
Object id is 7292, canonical name is ScalarFactorTransferRules.
Accessed 1569 times total.

Classification:

15A72 (Linear and multilinear algebra; matrix theory :: Vector and tensor algebra, theory of invariants)

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