Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those...
124 KB (12,666 words) - 15:19, 19 September 2024
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables...
75 KB (9,506 words) - 17:24, 21 June 2024
branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings. Algebraic may also refer to: Algebraic data type...
1 KB (238 words) - 13:14, 27 August 2020
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...
32 KB (4,185 words) - 14:05, 4 June 2024
mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...
11 KB (1,359 words) - 23:57, 25 May 2024
Linear algebra is the branch of mathematics concerning linear equations such as: a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...
64 KB (7,780 words) - 04:31, 11 August 2024
In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...
61 KB (10,459 words) - 23:14, 17 September 2024
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties...
20 KB (2,829 words) - 11:21, 17 April 2024
In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field) on a set X is a nonempty collection Σ of subsets of X...
30 KB (5,326 words) - 14:18, 11 September 2024
mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure...
22 KB (2,935 words) - 02:08, 13 August 2024
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
77 KB (12,096 words) - 18:17, 8 September 2024
In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...
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universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...
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mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...
64 KB (9,171 words) - 11:01, 7 August 2024
Algebraic notation is the standard method for recording and describing the moves in a game of chess. It is based on a system of coordinates to uniquely...
22 KB (2,606 words) - 03:04, 5 September 2024
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until...
120 KB (16,878 words) - 07:06, 26 July 2024
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the...
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algebra (also known as a Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is...
93 KB (13,918 words) - 12:02, 31 August 2024
mathematics, an algebraic expression is an expression built up from constants (usually, rational or algebraic numbers) variables, and the basic algebraic operations:...
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{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic:...
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In database theory, relational algebra is a theory that uses algebraic structures for modeling data, and defining queries on it with well founded semantics...
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The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...
50 KB (7,606 words) - 03:36, 9 September 2024
Borel set (redirect from Borel sigma algebra)
Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets...
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Ring (mathematics) (redirect from Ring (algebra))
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...
99 KB (13,632 words) - 06:07, 27 August 2024
Al-Khwarizmi (section Algebra)
equation), he has been described as the father or founder of algebra. The English term algebra comes from the short-hand title of his aforementioned treatise...
74 KB (7,467 words) - 03:54, 9 September 2024
Nonlinear algebra is the nonlinear analogue to linear algebra, generalizing notions of spaces and transformations coming from the linear setting. Algebraic geometry...
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A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in...
18 KB (1,762 words) - 01:24, 1 July 2024
Field (mathematics) (redirect from Field (algebra))
and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics...
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circle. Its Lie algebra is (more or less) the Witt algebra, whose central extension the Virasoro algebra (see Virasoro algebra from Witt algebra for a derivation...
64 KB (9,479 words) - 09:21, 13 September 2024
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with...
5 KB (545 words) - 03:03, 6 May 2024