What does eigenfunction mean?
Definitions for eigenfunction
eigen·func·tion
This dictionary definitions page includes all the possible meanings, example usage and translations of the word eigenfunction.
Wiktionary
eigenfunctionnoun
A function such that, for a given linear operator , for some scalar (called an eigenvalue).
Wikipedia
Eigenfunction
In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f {\displaystyle f} in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as for some scalar eigenvalue λ . {\displaystyle \lambda .} The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions. An eigenfunction is a type of eigenvector.
Wikidata
Eigenfunction
In mathematics, an eigenfunction of a linear operator, A, defined on some function space, is any non-zero function f in that space that returns from the operator exactly as is, except for a multiplicative scaling factor. More precisely, one has for some scalar, λ, the corresponding eigenvalue. The solution of the differential eigenvalue problem also depends on any boundary conditions required of . In each case there are only certain eigenvalues that admit a corresponding solution for when combined with the boundary conditions. Eigenfunctions are used to analyze . For example, is an eigenfunction for the differential operator for any value of, with corresponding eigenvalue . If boundary conditions are applied to this system, then only certain values of satisfy the boundary conditions, generating corresponding discrete eigenvalues . Specifically, in the study of signals and systems, the eigenfunction of a system is the signal which when input into the system, produces a response with the complex constant .
Numerology
Chaldean Numerology
The numerical value of eigenfunction in Chaldean Numerology is: 4
Pythagorean Numerology
The numerical value of eigenfunction in Pythagorean Numerology is: 7
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"eigenfunction." Definitions.net. STANDS4 LLC, 2024. Web. 16 Apr. 2024. <https://www.definitions.net/definition/eigenfunction>.
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