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In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by or , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be". [1] More precisely, given a function , the domain of f is X. In modern mathematical language, the domain is ...
t. e. In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.
Discrete valuation ring. In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an integral domain R that satisfies any one of the following equivalent conditions: R is a local principal ideal domain, and not a field. R is a valuation ring with a value ...
Piecewise function. In mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned into several intervals ("subdomains") on which the function may be defined differently. [1][2][3] Piecewise definition is actually a way of specifying ...
Frobenius endomorphism. In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic p, an important class that includes finite fields. The endomorphism maps every element to its p -th power.
In vector calculus, the Jacobian matrix (/ dʒəˈkoʊbiən /, [1][2][3] / dʒɪ -, jɪ -/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output ...
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