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So you can not define an individual vector
you must define a set, the vector space. all its members are vectors
in that set a sum of two vectors MUST be a vector for example.
wikipedia
A *vector space* (also called a *linear space*) is a collection of
objects called *vectors*, which may be added
<https://en.wikipedia.org/wiki/Vector_addition> together and multiplied
<https://en.wikipedia.org/wiki/Scalar_multiplication> ("scaled") by
numbers, called *scalars
<https://en.wikipedia.org/wiki/Scalar_(mathematics)>* in this context.
Scalars are often taken to be real numbers
<https://en.wikipedia.org/wiki/Real_number>, but there are also vector
spaces with scalar multiplication by complex numbers
<https://en.wikipedia.org/wiki/Complex_number>, rational numbers
<https://en.wikipedia.org/wiki/Rational_number>, or generally any field
<https://en.wikipedia.org/wiki/Field_(mathematics)>. The operations of
vector addition and scalar multiplication must satisfy certain
requirements, called *axioms <https://en.wikipedia.org/wiki/Axiom>*,
listed below <https://en.wikipedia.org/wiki/Vector_space#Definition>.
*Axiom**Meaning*Associativity
<https://en.wikipedia.org/wiki/Associativity> of addition*u* + (*v* + *w*)
= (*u* + *v*) + *w*Commutativity
<https://en.wikipedia.org/wiki/Commutativity> of addition*u* + *v* = *v*
+ *u*Identity element <https://en.wikipedia.org/wiki/Identity_element> of
additionThere exists an element *0* ∈ *V*, called the *zero vector
<https://en.wikipedia.org/wiki/Zero_vector>*, such that *v* + *0* = *v* for
all *v* ∈ *V*.Inverse elements
<https://en.wikipedia.org/wiki/Inverse_element> of additionFor every *v* ∈
V, there exists an element −*v* ∈ *V*, called the *additive inverse
<https://en.wikipedia.org/wiki/Additive_inverse>* of *v*, such that *v* +
(−*v*) = *0*.Compatibility
<https://en.wikipedia.org/wiki/Semigroup_action> of scalar multiplication
with field multiplication*a*(*b**v*) = (*ab*)*v* [nb 2]
<https://en.wikipedia.org/wiki/Vector_space#cite_note-3>Identity element
of scalar multiplication1*v* = *v*, where 1 denotes the multiplicative
identity <https://en.wikipedia.org/wiki/Multiplicative_identity> in *F*.
Distributivity <https://en.wikipedia.org/wiki/Distributivity> of scalar
multiplication with respect to vector addition *a*(*u* + *v*) = *a**u* +
*a**v*Distributivity of scalar multiplication with respect to field
addition(*a* + *b*)*v* = *a**v* + *b**v*
2015-10-23 23:18 GMT-03:00 Diego Saravia <dsa@unsa.edu.ar>:
2015-10-23 19:32 GMT-03:00 John Denker <jsd@av8n.com>:
On 10/23/2015 03:14 PM, Jeffrey Schnick wrote:
Sometimes a force can be represented by a vector.
a vector is a vector in a specific vector space
different lines of actions are diferent vector spaces in some cases
differents points of applications in other cases
or all the pysical space in others
perhaps these is usefull
https://en.wikipedia.org/wiki/Affine_space
--
Diego Saravia
Diego.Saravia@gmail.com
NO FUNCIONA->dsa@unsa.edu.ar
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