Traducción y análisis de palabras por inteligencia artificial ChatGPT
En esta página puede obtener un análisis detallado de una palabra o frase, producido utilizando la mejor tecnología de inteligencia artificial hasta la fecha:
- cómo se usa la palabra
- frecuencia de uso
- se utiliza con más frecuencia en el habla oral o escrita
- opciones de traducción
- ejemplos de uso (varias frases con traducción)
- etimología
Qué (quién) es eigenvalue - definición
![[[Eigenface]]s as examples of eigenvectors](https://commons.wikimedia.org/wiki/Special:FilePath/Eigenfaces.png?width=200 "[[Eigenface]]s as examples of eigenvectors")
![An extended version, showing all four quadrants]].](https://commons.wikimedia.org/wiki/Special:FilePath/Eigenvectors.gif?width=200 "An extended version, showing all four quadrants]].")
![PCA of the [[multivariate Gaussian distribution]] centered at <math>(1, 3)</math> with a standard deviation of 3 in roughly the <math>(0.878, 0.478)</math> direction and of 1 in the orthogonal direction. The vectors shown are unit eigenvectors of the (symmetric, positive-semidefinite) [[covariance matrix]] scaled by the square root of the corresponding eigenvalue. Just as in the one-dimensional case, the square root is taken because the [[standard deviation]] is more readily visualized than the [[variance]].](https://commons.wikimedia.org/wiki/Special:FilePath/GaussianScatterPCA.png?width=200 "PCA of the [[multivariate Gaussian distribution]] centered at <math>(1, 3)</math> with a standard deviation of 3 in roughly the <math>(0.878, 0.478)</math> direction and of 1 in the orthogonal direction. The vectors shown are unit eigenvectors of the (symmetric, positive-semidefinite) [[covariance matrix]] scaled by the square root of the corresponding eigenvalue. Just as in the one-dimensional case, the square root is taken because the [[standard deviation]] is more readily visualized than the [[variance]].")
![measurement]]. The center of each figure is the [[atomic nucleus]], a [[proton]].](https://commons.wikimedia.org/wiki/Special:FilePath/HAtomOrbitals.png?width=200 "measurement]]. The center of each figure is the [[atomic nucleus]], a [[proton]].")
![homothety]])](https://commons.wikimedia.org/wiki/Special:FilePath/Homothety in two dim.svg?width=200 "homothety]])")
![In this [[shear mapping]] the red arrow changes direction, but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it does not change direction, and since its length is unchanged, its eigenvalue is 1.](https://commons.wikimedia.org/wiki/Special:FilePath/Mona Lisa eigenvector grid.png?width=200 "In this [[shear mapping]] the red arrow changes direction, but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it does not change direction, and since its length is unchanged, its eigenvalue is 1.")
Wikipedia
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled.
Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.
