In basic mathematics, an operator is a symbol or function representing a mathematical operation.
In terms of vector spaces, an operator is a mapping from one vector space or module to another. Operators are of critical importance to both linear algebra and functional analysis, and they find application in many other fields of pure and applied mathematics. For example, in classical mechanics, the derivative is used ubiquitously, and in quantum mec...
More
In basic mathematics, an operator is a symbol or function representing a mathematical operation.
In terms of vector spaces, an operator is a mapping from one vector space or module to another. Operators are of critical importance to both linear algebra and functional analysis, and they find application in many other fields of pure and applied mathematics. For example, in classical mechanics, the derivative is used ubiquitously, and in quantum mechanics, observables are represented by linear operators. Important properties that various operators may exhibit include linearity, continuity, and boundedness.
Let U, V be two vector spaces. The mapping from U to V is called an operator. Let V be a vector space over the field K. We can define the structure of a vector space on the set of all operators from U to V:
for all A, B: U → V, for all x in U and for all α in K.
Additionally, operators from any vector space to itself form a unital associative algebra:
with the identity mapping (usually...
Less
