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- the word, as well as ''direction'' in space, is termed a [[../Vectors/|vector]], whereas [[../Vectors/|scalars]]. The typical case of a vector and, in fact, the intuitional ...14 KB (2,193 words) - 10:28, 11 October 2023
- ==Definitions of a vector== A vector is a mathematical concept that has both magnitude and direction. A vector is an ''object'' that has certain properties: ...2 KB (294 words) - 14:03, 5 May 2019
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- A '''differential graded Lie algebra''' is a graded <math>k</math>-vector space <math>\mathfrak{g}</math> ..., and it inherits a Lie bracket. (In fact, it is an <math>L_\infty</math>-algebra.) ...785 bytes (125 words) - 11:38, 26 March 2016
- ...be represented as [[matrices]] (or [[linear transformation]]s over some [[vector space]] over a [[field]]. ''See also: [[sl(n)]]'' ([[special linear Lie algebra]]) ...504 bytes (68 words) - 16:05, 21 February 2009
- ===A Noncommutative Quantum Observable Algebra is a Clifford Algebra=== ...math>, where <math>V</math> denotes a real [[../NormInducedByInnerProduct/|vector space]] and ...1 KB (215 words) - 06:05, 7 March 2022
- ===Preliminary data for the definition of a C*-Clifford algebra=== ...athcal{H}</math>, one can define an associated ''<math>C^*</math>-Clifford algebra'' , ...2 KB (399 words) - 09:49, 13 September 2020
- Let <math>X</math> and <math>Y</math> be two [[../NeutrinoRestMass/|vector fields]] on a smooth [[../NoncommutativeGeometry4/|manifold]] <math>M</math ...or2/|observables]] is taken to be the real [[../NormInducedByInnerProduct/|vector space]] of smooth functions on <math>M</math>, and with T being an element ...3 KB (465 words) - 15:32, 12 September 2020
- ...s global property, it admits an associated, unique--as well as finite--Lie algebra that completely specifies locally the properties of the Lie group everywher ...is not associative, and it is in fact a ''[[../NormInducedByInnerProduct/|vector space]]''. It is also perhaps this feature that makes the Lie algebras some ...4 KB (496 words) - 08:36, 11 March 2023
- ...rving diffeomorphisms of the circle. The representation theory of Virasoro algebra is rich, and has diverse applications in Mathematics and Physics. ''Vir'' is the Lie algebra over the field of complex numbers with the following generators: ...2 KB (251 words) - 23:03, 26 July 2017
- ...page presents and discusses an example of a non-associative {{lw|division algebra|}} over the [[real number]]s. ...a*b=\overline{ab}</math>. This is a commutative, non-associative division algebra of dimension 2 over the reals, and has no unit element. ...2 KB (292 words) - 21:31, 6 March 2022
- ...bilinear form is unique up to scaling. A Lie algebra is [[semi-simple Lie algebra|semi-simple]] if and only if its Killing form is [[non-degenerate]]. *<math>([x,y],z) = (x,[y,z])</math> where x,y,z are elements in the algebra and the brackets [] are the [[Lie brackets]] ...1 KB (187 words) - 03:09, 1 May 2017
- ...polynomial algebra <math>A[t]</math> is an essential tool to construct an algebra extension <math>B</math> of <math>A</math> in which a given <math>z\in A</m === Remark: Algebra expansion === ...7 KB (1,005 words) - 00:24, 16 June 2024
- ===Vector spaces, vector operations, matrix operations=== ...ught of as two-dimensional arrays of elements from the scalar field of our vector space. ...2 KB (239 words) - 10:03, 14 January 2024
- +Linear algebra (Matrices, Vector algebra). +Vector calculus. ...2 KB (235 words) - 01:15, 26 July 2017
- ...ion <math>f:U\rightarrow V </math> from a vector space <math>U</math> to a vector space <math>V</math> is called a '''linear map''' if ...se that the function <math>A</math> is "compatible" with the operations of vector addition and scalar multiplication. The significance of these properties ma ...2 KB (285 words) - 12:42, 3 December 2022
- A ket is just another way to write a column vector. If you have a vector called <math>v</math>, you can write it as <math>\vec{v}</math>, as <nowiki If you transpose a column vector you obtain a row vector. Dirac's way to write row vectors are Bras: <math>\langle v|</math>. Bra an ...3 KB (595 words) - 03:11, 22 June 2017
- ===Vector=== A {\mathbf vector} is a quantity which is considered as possessing ''direction'' as well as ...4 KB (630 words) - 03:50, 13 September 2020
- <small>[[Linear algebra]]</small> ...ar algebra is a branch of mathematics that studies objects called vectors, vector spaces, linear equations, linear maps, and matrices. It also studies how th ...4 KB (649 words) - 15:18, 13 January 2024
- ...on-commutative]]) [[../QuantumSpinNetworkFunctor2/|observable]] (Clifford) Algebra} ...se [[../Vectors/|vector]]''-- defined as <math><{\phi}|</math> (or ''"bra" vector'' ). Thus, a ""bra-ket'' '' is defined as the [[../NormInducedByInnerProduc ...2 KB (220 words) - 05:06, 12 September 2020
- ...tly, a specific ''algebra'' consists of a [[../NormInducedByInnerProduct/|vector space]] <math>E</math> over a ground [[../CosmologicalConstant/|field]] (ty A ''Jordan algebra'' (over <math>\bR</math>), is an algebra over <math>\bR</math> for which: ...10 KB (1,513 words) - 15:39, 12 September 2020
- ..., linear maps between vector spaces, and matrices.<ref>[[Wikipedia: Linear algebra]]</ref> *'''[[Linear algebra (Osnabrück 2024-2025)/Part I]]''' ...6 KB (897 words) - 18:11, 14 October 2024
- [[File:Algebra extension.svg|thumb|Algebra extension <math>B</math> of <math>A</math> containing an inverse element <m ...nsider, among other things, topological properties that allow to create an algebra extension <math>B</math> in which an multiplicative inverse of a given elem ...11 KB (1,584 words) - 19:24, 1 March 2025