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- ...igh school algebra. [[Group]]s, [[ring]]s, [[field]]s, [[module]]s, and [[vector space]]s are common objects of study in higher algebra. Modern algebra also arguably contains the field of [[number theory]], which has important applications in computer science.6 KB (866 words) - 06:57, 17 January 2025
- ...igh school algebra. [[Group]]s, [[ring]]s, [[field]]s, [[module]]s, and [[vector space]]s are common objects of study in higher algebra. Modern algebra also arguably contains the field of [[number theory]], which has important applications in computer science.3 KB (369 words) - 20:18, 18 June 2021
- ...lso most abstractly, a vector is any object which is an element of a given vector space. ...\,y\,\,z\,\,...)</math>. The set of vectors over a [[field]] is called a [[vector space]].11 KB (1,875 words) - 14:35, 7 January 2025
- ...cally closed]] [[field]]s, but it can also be done more generally over any field or even over [[ring]]s. It is not to be confused with [[analytic geometry]] ...dimension]] <math>n</math> over an algebraically closed field, such as the field <math>\mathbb{C}</math> of [[complex number]]s. (We can think of this as <m2 KB (361 words) - 00:59, 24 January 2020
- ====4.1.2: Eigenvalue/vector bash==== ...he domain of <math>\hat{T}</math> where everything gets mapped to the null vector.15 KB (2,406 words) - 22:56, 23 November 2023
- ...d to be a '''field extension'''. We sometimes say that <math>L</math> is a field extension of <math>K</math>. ...hought of as a [[vector space]] over <math>K</math>. The dimension of this vector space is called the ''degree'' of the extension, and is denoted by <math>[L2 KB (362 words) - 23:46, 24 March 2009
- ...<math>F</math> consists of a [[set]] (of [[vector]]s) and two operations, vector addition and [[scalar]] multiplication, which obey the following rules: ==Axioms of vector space==3 KB (561 words) - 23:47, 20 March 2009
- ...avier-Stokes equations must be found with the help of computers. This is a field of sciences by its own called computational fluid dynamics. ...osity, and <math>f_i</math> be the <math>i</math>th component of the force field, the equations are:3 KB (553 words) - 21:08, 2 May 2022
- A '''matrix''' over a field <math>F</math> is a [[function]] from <math>A\times B</math> to <math>F</ma ...rray of scalars from the [[field]], such that each column belongs to the [[vector space]] <math>F^m</math>, where <math>m</math> is the number of rows. If a4 KB (856 words) - 14:29, 30 March 2013
- ...ral algebraic structures, such as [[group]]s, [[ring]]s, [[field]]s, and [[vector space]]s. While there is little risk of confusion, mathematicians use the *[[Field]]494 bytes (65 words) - 17:21, 28 September 2024
- ...ar constraint over a [[vector space]] <math>\mathbb{F}^n</math> for some [[field]] <math>\mathbb{F}</math>: where <math>(x_1,...,x_n)</math> is an element of the vector space and <math>c_1,...,c_n,c</math> are scalars.2 KB (445 words) - 07:16, 21 August 2009
- ...[[field]] with two elements, <math>F_2</math>. Let <math>V</math> be the [[vector space]] of all such functions. Define the linear operator <math>A : V \to V13 KB (2,414 words) - 13:37, 11 July 2016
- ...ll morphisms are injective, and so they can be viewed as [[field extension|field extensions]]). * The category '''Vect''' of all [[vector space|vector spaces]], where morphisms are [[linear map|linear maps]].5 KB (792 words) - 18:01, 7 April 2012
- ...h as the action of a group on a [[vector space]], a group, a [[ring]], a [[field]], a [[graph]], etc.). This can be done rigorously in the language of [[cat For instance, by this definition, a group action on a [[vector space]], <math>V</math> (also known as a [[group representation]]) is a gro5 KB (917 words) - 20:17, 7 September 2008
- ...ntly in [[abstract algebra]]. It is a generalization of the concept of a [[vector space]]. If <math>R</math> is a [[field]] then <math>M</math> is a vector space over <math>R</math>.883 bytes (156 words) - 19:11, 23 January 2017
- * [[Vector space]] * [[Field]]1 KB (227 words) - 16:19, 8 September 2009
- [[field]]s, and [[vector space]]s)—are special cases of this1 KB (234 words) - 22:30, 18 May 2009
- Suppose <math>A</math> is a <math>n \times n</math> [[matrix]] (over a field <math>K</math>). Then the characteristic polynomial of <math>A</math> is de An [[eigenvector]] <math>\bold{v} \in K^n</math> is a non-zero vector that satisfies the relation <math>A\bold{v} = \lambda\bold{v}</math>, for s19 KB (3,412 words) - 13:57, 21 September 2022
- ...h>v_1, v_2, \ldots, v_n</math> in a [[vector space]] <math>V</math> over a field <math>K</math> are '''linearly independent''' if there do not exist scalars ..._n\}</math> are a basis, then <math>\{v_1, \ldots, v_n, w\}</math> for any vector <math>w \in V</math> are linearly dependent.2 KB (300 words) - 22:35, 16 March 2010
- ...olving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image: ...d out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The21 KB (3,334 words) - 22:53, 23 March 2022