# eigenfunction Definition and Topics - 7 Discussions

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function 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

D
f
=
λ
f

{\displaystyle Df=\lambda f}
for some scalar eigenvalue λ. 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.

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1. ### I Differences between the PCA function and Karhunen-Loève expansion

Hello everyone. I am currently using the pca function from matlab on a gaussian process. Matlab's pca offers three results. Coeff, Score and Latent. Latent are the eigenvalues of the covariance matrix, Coeff are the eigenvectors of said matrix and Score are the representation of the original...
2. ### Eigenstates of a free electron in a uniform magnetic field

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3. ### Eigensolution of the wave function in a potential field.

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4. ### A Confusing eigensolutions of a wave function

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5. ### Schrodinger equation and boundary conditions

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6. ### Why are we only considering the first eigenfrequencies?

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7. ### A Convolution operator spectrum

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