linear operator (Meaning)
Wordnet
linear operator (n)
an operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions)
Synonyms & Antonyms of linear operator
No Synonyms and anytonyms found
linear operator Sentence Examples
- A linear operator is a function that satisfies the properties of linearity: additivity and homogeneity.
- The derivative operator is a linear operator on the space of differentiable functions.
- The Laplacian operator is a linear operator on the space of twice differentiable functions.
- The Fourier transform is a linear operator on the space of square-integrable functions.
- The matrix representation of a linear operator is a matrix with the property that each column is a multiple of the corresponding basis vector.
- The spectrum of a linear operator is the set of eigenvalues of the operator.
- The adjoint of a linear operator is another linear operator that satisfies the property of linearity and the adjoint relationship.
- The inverse of a linear operator is another linear operator that satisfies the property that the composition of the two operators is the identity operator.
- The determinant of a linear operator is a scalar that is equal to the product of the eigenvalues of the operator.
- The trace of a linear operator is a scalar that is equal to the sum of the eigenvalues of the operator.
FAQs About the word linear operator
an operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions)
No synonyms found.
No antonyms found.
A linear operator is a function that satisfies the properties of linearity: additivity and homogeneity.
The derivative operator is a linear operator on the space of differentiable functions.
The Laplacian operator is a linear operator on the space of twice differentiable functions.
The Fourier transform is a linear operator on the space of square-integrable functions.
