Eigenvector

lastmod 2018-08-17created 2016-10-261 edits

In linear algebra, an eigenvector (固有vector) of a linear transformation is a nonzero vector whose direction does not change after the linear transformation is applied. The factor by which the length of the eigenvector changes is called the eigenvalue (固有 value[*]) of the linear transformation corresponding to that eigenvector. A linear transformation can usually be fully described by its eigenvectors and their eigenvalues alone.

The concepts of eigenvectors and eigenvalues hold an important place in many fields of applied mathematics, and are used frequently in linear algebra, functional analysis, and various nonlinear fields.

See also

• Linear algebra
• vector

Favorite site

• Wikipedia (en) Eigenvalues and eigenvectors
• An introductory lecture on Eigenvectors, PCA, Covariance, and Entropy ¹

References