linear operator Synonyms

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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

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

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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.