Difference between revisions of "Vector space"

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A '''vector space''' is a subject in advanced calculus that deals with dimensions beyond the simple x-y axis.  Vector spaces typically focus on the relationship of direction rather than distance.
A '''vector space''' is an additive [[Group (mathematics)|group]] in which addition is [[commutative]] and with which is associated a [[Field (mathematics)|field]] of scalars, as the field of real [[number]]s, such that the product of a scalar and an element of the group or a vector is defined, the product of two scalars times a vector is [[associative]], one times a vector is the vector, and two distributive [[law]]s hold.
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The formal definition of a '''vector space''' is an additive [[Group (mathematics)|group]] in which addition is [[commutative]] and with which is associated a [[Field (mathematics)|field]] of scalars, as the field of real [[number]]s, such that the product of a scalar and an element of the group or a vector is defined, the product of two scalars times a vector is [[associative]], one times a vector is the vector, and two distributive [[law]]s hold.
  
 
[[Category:Algebra]]
 
[[Category:Algebra]]

Revision as of 14:04, 31 October 2009

A vector space is a subject in advanced calculus that deals with dimensions beyond the simple x-y axis. Vector spaces typically focus on the relationship of direction rather than distance.

The formal definition of a vector space is an additive group in which addition is commutative and with which is associated a field of scalars, as the field of real numbers, such that the product of a scalar and an element of the group or a vector is defined, the product of two scalars times a vector is associative, one times a vector is the vector, and two distributive laws hold.