linear operator Synonyms

No Synonyms and anytonyms found

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)

linear operator Sentence Examples

1. A linear operator is a function that satisfies the properties of linearity: additivity and homogeneity.
2. The derivative operator is a linear operator on the space of differentiable functions.
3. The Laplacian operator is a linear operator on the space of twice differentiable functions.
4. The Fourier transform is a linear operator on the space of square-integrable functions.
5. The matrix representation of a linear operator is a matrix with the property that each column is a multiple of the corresponding basis vector.
6. The spectrum of a linear operator is the set of eigenvalues of the operator.
7. The adjoint of a linear operator is another linear operator that satisfies the property of linearity and the adjoint relationship.
8. 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.
9. The determinant of a linear operator is a scalar that is equal to the product of the eigenvalues of the operator.
10. 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

What is the meaning of the word linear operator

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

What are the synonyms of the word linear operator

No synonyms found.

What are the antonyms of the word linear operator

No antonyms found.

What is the usage of word linear operator

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.

How to use the word linear operator in a sentence?

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.