Difference between revisions of "Vector space"
From Conservapedia
(Needs rewriting badly.) |
(improved introduction; more improvements welcome) |
||
| Line 1: | Line 1: | ||
| − | + | 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. | + | |
| + | 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 20:04, October 31, 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.
