Algebraic Properties on V_n

==2024-11-18

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Properties are the foundation of deriving applications.

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Theory

In n-Dimensional Space for all $u,v,w\in V_n$ and all scalars $c\&d$,

Commutative Property

$u+v=v+u$

Associative Property

$(u+v)+w=u+(v+w)$

Additive Identity Property

$u+\bar{0}=u=\bar{0}+u$

Additive Inverse Property

$u+(-u)=(-u)+u=\bar{0}$

Distributive Property

$(c+d)u=cu+du$ $c(u+v)=cu+cv$

Associative Property

$c(du)=(cd)u$

Multiplicative Identity Property

$1.u=u$

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Examples

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PTR