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scalar 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 u→normal-→u\vec{u}, v→normal-→v\vec{v}.  Then such a scalar rrr can be transferred from a vector to the other vector and to the whole product.  This is true for scalar product,

u→⋅(r⁢v→)=(r⁢u→)⋅v→=r⁢(u→⋅v→),normal-⋅normal-→urnormal-→vnormal-⋅rnormal-→unormal-→vrnormal-⋅normal-→unormal-→v\vec{u}\!\cdot\!(r\vec{v})=(r\vec{u})\!\cdot\!\vec{v}=r(\vec{u}\!\cdot\!\vec{v% }),

for vector product,

u→×(r⁢v→)=(r⁢u→)×v→=r⁢(u→×v→),normal-→urnormal-→vrnormal-→unormal-→vrnormal-→unormal-→v\vec{u}\!\times\!(r\vec{v})=(r\vec{u})\!\times\!\vec{v}=r(\vec{u}\!\times\!% \vec{v}),

and also for dyad product,

u→⁢(r⁢v→)=(r⁢u→)⁢v→=r⁢(u→⁢v→).normal-→urnormal-→vrnormal-→unormal-→vrnormal-→unormal-→v\vec{u}(r\vec{v})=(r\vec{u})\vec{v}=r(\vec{u}\vec{v}).
Keywords: 
scalar multiplication
Synonym: 
transfer rules of scalar factor
Major Section: 
Reference
Type of Math Object: 
Topic
Parent: 
Euclidean vector

Mathematics Subject Classification

15A72 Vector and tensor algebra, theory of invariants

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Info

Owner: pahio
Added: 2005-08-04 - 19:17
Author(s): pahio

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(v5) by pahio 2013-03-22
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