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A vector whose direction is unchanged by a given transformation and whose magnitude is changed by a factor corresponding to that vector's eigenvalue. In quantum mechanics, the transformations involved are operators corresponding to a physical system's observables. The eigenvectors correspond to possible states of the system, and the eigenvalues to possible observed values.

[Partial translation of German Eigenvektor : eigen-, characteristic; see eigenvalue + Vektor, vector.]


(Mathematics) maths physics a vector x satisfying an equation Ax = λx, where A is a square matrix and λ is a constant
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They cover vectors, matrices, determinants, eigenvalues and eigenvectors, some applications of matrices and determinants, and matrix series and additional properties of matrices.
The eigenvalues and eigenvectors of S are calculated as follows:
In mathematical terms, the principal components of the distribution of faces or the eigenvectors of the covariance matrix of the set of face images, is sought by treating an image as a vector in a very high dimensional face space.
M-1]] contains M eigenvectors that span the signal subspace of the correlation matrix, the noise eigenvector matrix [E.
Finally, the eigenvectors was accurately identify through improved Gustafson-Kessell (IGK).
Reanalysis methods estimate the eigenvalues and eigenvectors of a modified design without performing a full-order eigenvalue analysis.
Eigen countenances are a situated of eigenvectors utilized as a part of the PC Vision issue of human face acknowledgment.
Reanalysis methods use a basis composed of eigenvectors from both the baseline and the modified designs which are in general linearly dependent.
Then, the gKDR proposes the eigenvectors of M(p + q) x M(p + q) symmetric matrix:
These properties are rank of the matrices A, B and C and eigenvectors of these matrices which correspond to the egenvalue zero.
Eryilmaz [6] studied q-Sturm-Liouville boundary value problem in the Hilbert space with a spectral parameter in the boundary condition and he proved theorems on the completeness of the system of eigenvalues and eigenvectors of operator by Pavlov's method.