eigenvalue

As a noun eigenvalue

is (linear algebra) a scalar, $\backslash lambda\backslash !$, such that there exists a vector $x$ (the corresponding eigenvector) for which the image of $x$ under a given linear operator $\backslash rm\; a\backslash !$ is equal to the image of $x$ under multiplication by $\backslash lambda$; ie $\{\backslash rm\; a\}\; x\; =\; \backslash lambda\; x\backslash !$.

As an adjective undefined is

lacking a definition or value.

As nouns the difference between eigenvalue and eigenfunctions

is that eigenvalue is (linear algebra) a scalar, $\backslash lambda\backslash !$, such that there exists a vector $x$ (the corresponding eigenvector) for which the image of $x$ under a given linear operator $\backslash rm\; a\backslash !$ is equal to the image of $x$ under multiplication by $\backslash lambda$; ie $\{\backslash rm\; a\}\; x\; =\; \backslash lambda\; x\backslash !$ while eigenfunctions is .

Eigenvalue is a related term of eigenstate.

As nouns the difference between eigenstate and eigenvalue

is that eigenstate is a dynamic quantum mechanical state whose wave function is an eigenvector that corresponds to a physical quantity while eigenvalue is a scalar, $\backslash lambda\backslash !$, such that there exists a vector $x$ (the corresponding eigenvector) for which the of $x$ under a given linear operator $\backslash rm\; A\backslash !$ is equal to the of $x$ under multiplication by $\backslash lambda$; i.e. $\{\backslash rm\; A\}\; x\; =\; \backslash lambda\; x\backslash !$

As nouns the difference between scalar and eigenvalue

is that scalar is (mathematics) a quantity that has magnitude but not direction; compare vector while eigenvalue is (linear algebra) a scalar, $\backslash lambda\backslash !$, such that there exists a vector $x$ (the corresponding eigenvector) for which the image of $x$ under a given linear operator $\backslash rm\; a\backslash !$ is equal to the image of $x$ under multiplication by $\backslash lambda$; ie $\{\backslash rm\; a\}\; x\; =\; \backslash lambda\; x\backslash !$.

As an adjective scalar

is (mathematics) having magnitude but not direction.

Eugenfunction is often a misspelling of eigenvalue.

Eugenfunction has no English definition.

As a noun eigenvalue

is a scalar, $\backslash lambda\backslash !$, such that there exists a vector $x$ (the corresponding eigenvector) for which the of $x$ under a given linear operator $\backslash rm\; A\backslash !$ is equal to the of $x$ under multiplication by $\backslash lambda$; i.e. $\{\backslash rm\; A\}\; x\; =\; \backslash lambda\; x\backslash !$

As a noun eigenvalue

is (linear algebra) a scalar, $\backslash lambda\backslash !$, such that there exists a vector $x$ (the corresponding eigenvector) for which the image of $x$ under a given linear operator $\backslash rm\; a\backslash !$ is equal to the image of $x$ under multiplication by $\backslash lambda$; ie $\{\backslash rm\; a\}\; x\; =\; \backslash lambda\; x\backslash !$.

As an adjective positone is

(mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.

As nouns the difference between eigenvalue and eigengap

is that eigenvalue is a scalar, $\backslash lambda\backslash !$, such that there exists a vector $x$ (the corresponding eigenvector) for which the of $x$ under a given linear operator $\backslash rm\; A\backslash !$ is equal to the of $x$ under multiplication by $\backslash lambda$; i.e. $\{\backslash rm\; A\}\; x\; =\; \backslash lambda\; x\backslash !$eigengap is the difference between successive eigenvalues.

As nouns the difference between eigenvalue and eigensolver

is that eigenvalue is (linear algebra) a scalar, $\backslash lambda\backslash !$, such that there exists a vector $x$ (the corresponding eigenvector) for which the image of $x$ under a given linear operator $\backslash rm\; a\backslash !$ is equal to the image of $x$ under multiplication by $\backslash lambda$; ie $\{\backslash rm\; a\}\; x\; =\; \backslash lambda\; x\backslash !$ while eigensolver is a program or algorithm that calculates eigenvalues or eigenvectors.