Eigenfunction in a sentence
Synonym: function.
Meaning: A function that remains unchanged except for a multiplicative factor when an operator is applied; often used in mathematics.
(1) The eigenfunction of a symmetric matrix is always real-valued.
(2) The eigenfunction of a unitary operator preserves the norm of a vector.
(3) The eigenfunction of the given matrix is a complex exponential function.
(4) The eigenfunction of a Fourier transform is a complex exponential function.
(5) The eigenfunction of a Hermitian matrix can be used to diagonalize the matrix.
(6) The eigenfunction of a symmetric matrix can be used to diagonalize the matrix.
(7) The eigenfunction of the quantum harmonic oscillator is a Gaussian wave packet.
(8) The eigenfunction of a Hermitian matrix can be used to compute its eigenvalues.
(9) The eigenfunction of a linear operator satisfies a specific eigenvalue equation.
(10) The eigenfunction was normalizable, indicating a valid solution to the equation.
Eigenfunction sentence
(11) The eigenfunction of a normal operator is orthogonal to all other eigenfunctions.
(12) The eigenfunction of a self-adjoint operator is associated with a real eigenvalue.
(13) The eigenfunction of a unitary operator is orthogonal to all other eigenfunctions.
(14) The eigenfunction of a Hermitian operator is orthogonal to all other eigenfunctions.
(15) The eigenfunction of a Hermitian operator forms a complete set in the Hilbert space.
(16) The eigenfunction of a self-adjoint operator is associated with a unique eigenvalue.
(17) The eigenfunction of a Sturm-Liouville problem satisfies certain boundary conditions.
(18) The eigenfunction of a Hermitian matrix is a vector that satisfies certain conditions.
(19) The eigenfunction of a linear operator is a function that is unchanged by the operator.
(20) The eigenfunction of a linear operator can be used to solve a system of linear equations.
Eigenfunction make sentence
(21) The eigenfunction of a Laplace-Beltrami operator represents a possible shape of a surface.
(22) The eigenfunction of a quantum mechanical operator represents a possible state of a system.
(23) The eigenfunction of the Laplace operator is a fundamental concept in mathematical physics.
(24) The eigenfunction of a differential equation represents a possible solution to the equation.
(25) The eigenfunction of a symmetric differential operator is associated with a real eigenvalue.
(26) The eigenfunction of a linear operator can be used to find the eigenvectors of the operator.
(27) The eigenfunction of a quantum mechanical system determines the energy levels of the system.
(28) The eigenfunction of a differential equation is a solution that satisfies certain conditions.
(29) The eigenfunction of the Laplace operator is a solution to the corresponding eigenvalue problem.
(30) The eigenfunction of a Hermitian operator can be used to construct a complete orthonormal basis.
Sentence of eigenfunction
(31) The eigenfunction of a linear operator can be used to decompose a vector into its eigencomponents.
(32) The eigenfunction of a linear transformation is a vector that is only scaled by the transformation.
(33) The eigenfunction of a Sturm-Liouville problem is a function that satisfies certain boundary conditions.
(34) The eigenfunction of a time-independent Hamiltonian operator represents a stationary state of a quantum system.
(35) The eigenfunction of a linear transformation represents a direction in which the transformation acts as a scalar multiplication.
(36) The eigenfunction of a partial differential equation is a function that satisfies certain boundary conditions and determines the behavior of the system.
Eigenfunction meaning
Eigenfunction is a mathematical term that refers to a function that satisfies a certain equation. Specifically, an eigenfunction is a function that, when multiplied by a constant, remains unchanged. This constant is known as the eigenvalue, and it is a crucial component of the eigenfunction. If you are studying mathematics or physics, you will likely come across the term eigenfunction at some point. Here are some tips for how to use this word in a sentence:
1. Start with a definition: If you are introducing the term eigenfunction to someone who is unfamiliar with it, start by defining it.
For example, "An eigenfunction is a function that satisfies a certain equation and remains unchanged when multiplied by a constant."
2. Use it in context: To help someone understand the concept of an eigenfunction, it can be helpful to use it in a sentence that provides context.
For example, "The eigenfunction of a quantum mechanical system represents the probability distribution of the system's energy states."
3. Explain its significance: Eigenfunctions are important in many areas of mathematics and physics, so it can be helpful to explain why they are significant.
For example, "Eigenfunctions are used to solve differential equations, which are fundamental to many areas of science and engineering."
4. Use it in a problem: If you are working on a math or physics problem that involves eigenfunctions, use the term in a sentence that describes the problem.
For example, "To solve this differential equation, we need to find the eigenfunctions and eigenvalues of the operator."
5. Compare and contrast: If you are discussing multiple concepts that are related to eigenfunctions, it can be helpful to compare and contrast them.
For example, "Eigenfunctions are similar to eigenvectors, but instead of representing a vector that is unchanged by a linear transformation, they represent a function that is unchanged by a multiplication."
Overall, using the term eigenfunction in a sentence requires a solid understanding of its definition and significance. By providing context, explaining its significance, and using it in a problem or comparison, you can help others understand this important mathematical concept.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Eigenfunction. They do not represent the opinions of TranslateEN.com.