linear operator

Noun

Meaning

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

Synonyms

Hypernyms

Examples

A linear operator itself does not actually depend on a basis: it is just a linear map that accepts a vector as an argument and produces another vector. Source: Internet

A function which satisfies these properties is called a linear function (or linear operator, or more generally a linear map ). Source: Internet

Because the Laplace transform is a linear operator, * The Laplace transform of a sum is the sum of Laplace transforms of each term. :: * The Laplace transform of a multiple of a function is that multiple times the Laplace transformation of that function. Source: Internet

;Convolution of a test function with a distribution If f ∈ D(R n ) is a compactly supported smooth test function, then convolution with f, : defines a linear operator which is continuous with respect to the LF space topology on D(R n ). Source: Internet

For the individual matrix entries, this transformation law has the form so the tensor corresponding to the matrix of a linear operator has one covariant and one contravariant index: it is of type (1,1). Source: Internet

Each observable is represented by a maximally Hermitian (precisely: by a self-adjoint ) linear operator acting on the state space. Source: Internet

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