Binary operations

In mathematics, a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g); it produces a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

In mathematics and vector calculus, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R3) and is denoted by the symbol ×.

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from elementary algebra.

In mathematics, a discrete logarithm is an integer k solving the equation bk = g, where b and g are elements of a finite group.

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n.

Multiplication (often denoted by the cross symbol "×", by a point "·", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division.

In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure.

Idempotence (/ˌaɪdᵻmˈpoʊtəns/ EYE-dəm-POH-təns) is the property of certain operations in mathematics and computer science, that can be applied multiple times without changing the result beyond the initial application.

In mathematics, the tensor product, denoted by ⊗, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules, among many other structures or objects.

In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, and is defined as iterated exponentiation.

In abstract algebra, alternativity is a property of a binary operation.

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set (more formally, an operation whose arity is two, and whose two domains and one codomain are (subsets of) the same set).

In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms of linear maps (module homomorphisms).