Linear Operator

linear operator

[′lin·ē·ər ′äp·ə‚rād·ər] (mathematics) linear transformation

Linear Operator

a generalization of the concept of linear transformation to vector spaces. F is called a linear operator on a vector space E if it is a function on E with values in some vector space E₁ and has the linearity property

F(αx + βy) = αF(x) + βF(y)

where x and y are elements of E, and α and β are numbers. If the E and E₁ are normed spaces and ǀǀF(x)ǀǀ / ǀǀxǀǀ is uniformly bounded for all x ∈ E, then the linear operator F is said to be bounded and

is called its norm.

The most important linear operators on function spaces are the differential linear operators

and the integral linear operators

The Laplace operator is an example of a linear operator on a space of functions of many variables. The theory of linear operators finds numerous applications in various problems of mathematical physics and applied mathematics.

linear operator

Linear Operator

linear operator

Linear Operator

linear operator

Words related to linear operator

noun an operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions)

Related Words