In mathematics, a basic algebraic operation is any one of the common operations of elementary algebra, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power).[1] These operations may be performed on numbers, in which case they are often called arithmetic operations. They may also be performed, in a similar way, on variables, algebraic expressions,[2] and more generally, on elements of algebraic structures, such as groups and fields.[3] An algebraic operation may also be defined simply as a function from a Cartesian power of a set to the same set.[4]
The term algebraic operation may also be used for operations that may be defined by compounding basic algebraic operations, such as the dot product. In calculus and mathematical analysis, algebraic operation is also used for the operations that may be defined by purely algebraic methods. For example, exponentiation with an integer or rational exponent is an algebraic operation, but not the general exponentiation with a real or complex exponent. Also, the derivative is an operation that is not algebraic.
^William Smyth, Elementary algebra: for schools and academies, Publisher Bailey and Noyes, 1864, "Algebraic Operations"
^Horatio Nelson Robinson, New elementary algebra: containing the rudiments of science for schools and academies, Ivison, Phinney, Blakeman, & Co., 1866, page 7
^"Algebraic operation - Encyclopedia of Mathematics". encyclopediaofmath.org. Retrieved 2020-08-27.
and 27 Related for: Algebraic operation information
In mathematics, a basic algebraicoperation is any one of the common operations of elementary algebra, which include addition, subtraction, multiplication...
universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...
empirical sciences. Algebra is the branch of mathematics that studies algebraicoperations and algebraic structures. An algebraic structure is a non-empty...
expressed as algebraic equations. In mathematics, a basic algebraicoperation is any one of the common operations of elementary algebra, which include...
calculators with algebraic entry system with parentheses (AESP) support the entry of parentheses. An input scheme known as algebraic operating system...
mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraicoperations (addition, subtraction...
connection between his algebra and logic was later put on firm ground in the setting of algebraic logic, which also studies the algebraic systems of many other...
probability distribution of a random variable obtained after performing algebraicoperations are not straightforward. Therefore, the behavior of the different...
In mathematics, the dot product or scalar product is an algebraicoperation that takes two equal-length sequences of numbers (usually coordinate vectors)...
an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic expressions...
operator, a notation used to signify multiplication Dot product, algebraicoperation returning a single number from two equal-length sequences The Dot...
contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically using a finite...
mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings...
equivalence relation on an algebraic object that is compatible with the algebraic structure, in the sense that the operations are well-defined on the equivalence...
calculations, involving these operations and relations. Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator...
types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures...
In universal algebra, an algebra (or algebraic structure) is a set A together with a collection of operations on A. An n-ary operation on A is a function...
representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraicoperations (for example, matrix addition...
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...
Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebraoperations such as...
coefficients are algebraic numbers is again algebraic. That can be rephrased by saying that the field of algebraic numbers is algebraically closed. In fact...
both Huntington in 1904 and Leibniz in 1890 used the symbol as an algebraicoperation. Furthermore, Huntington in 1904 used the symbol as inclusive disjunction...
mathematics, vector algebra may mean: The operations of vector addition and scalar multiplication of a vector space The algebraicoperations in vector calculus...
Look up algebraic in Wiktionary, the free dictionary. Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic...
mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus...
an Adams operation, denoted ψk for natural numbers k, is a cohomology operation in topological K-theory, or any allied operation in algebraic K-theory...
multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). In common geometrical...