Linear algebra - Revision history

Karl Jones at 12:03, 28 May 2016

2016-05-28T12:03:36Z

Karl Jones: /* See also */

2016-05-28T12:00:21Z

‎See also

Karl Jones: /* Pure and applied mathematics */

2016-04-15T17:10:30Z

‎Pure and applied mathematics

Karl Jones: Created page with "'''Linear algebra''' is the branch of mathematics concerning vector spaces and linear mappings between such spaces. == Description == It includes the study of lines, pla..."

2016-04-15T17:10:14Z

Created page with "'''Linear algebra''' is the branch of mathematics concerning vector spaces and linear mappings between such spaces. == Description == It includes the study of lines, pla..."

New page

'''Linear algebra''' is the branch of [[mathematics]] concerning vector spaces and linear mappings between such spaces.

== Description ==

It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.

The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns.

Such equations are naturally represented using the formalism of matrices and vectors.

== Pure and applied mathematics ==

Linear algebra is central to both [[pure mathematics]] and [[applied mathematics]].

For instance, [[abstract algebra]] arises by relaxing the axioms of a vector space, leading to a number of generalizations.

]]Functional analysis]] studies the infinite-dimensional version of the theory of vector spaces.

Combined with [[calculus]], linear algebra facilitates the solution of [[linear systems]] of [[differential equations]].

Techniques from linear algebra are also used in [[analytic geometry]], [[engineering]], [[physics]], [[natural sciences]], [[computer science]], [[computer animation]], and the social sciences (particularly in economics).

Because linear algebra is such a well-developed theory, [[nonlinear mathematical models]] are sometimes approximated by linear models.

== See also ==

* [[Mathematics]]
* [[Matrix (mathematics)]]

== External links ==

* [https://en.wikipedia.org/wiki/Linear_algebra Linear algebra] @ Wikipedia

[[Category:Linear algebra]]
[[Category:Mathematics]]
[[Category:Matrices]]

← Older revision		Revision as of 12:03, 28 May 2016
Line 1:		Line 1:
−	'''Linear algebra''' is the branch of [[mathematics]] concerning vector spaces and linear mappings between such spaces.	+	[[File:Linear subspaces with shading.svg.png\|thumb\|The three-dimensional [[Euclidean space]] '''R3''' is a [[vector space]], and lines and planes passing through the origin are vector subspaces in '''R3'''.]]'''Linear algebra''' is the branch of [[mathematics]] concerning vector spaces and linear mappings between such spaces.

	== Description ==		== Description ==

@@ Line 25: / Line 25: @@
 == See also ==
 * [[Mathematics]]
 * [[Matrix (mathematics)]]
 == External links ==

@@ Line 15: / Line 15: @@
 For instance, [[abstract algebra]] arises by relaxing the axioms of a vector space, leading to a number of generalizations.
-]]Functional analysis]] studies the infinite-dimensional version of the theory of vector spaces.
+[[Functional analysis]] studies the infinite-dimensional version of the theory of vector spaces.
 Combined with [[calculus]], linear algebra facilitates the solution of [[linear systems]] of [[differential equations]].