Eigenvalues and eigenvectors
Eigenvalues and eigenvectors In linear algebra , an eigenvector ( / ˈ aɪ ɡ ə n ˌ v ɛ k t ər / ) 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. [1] Loosely speaking, in a multidimensional vector space , the eigenvector is not rotated. Formal definition [ edit ] If T is a linear transformation from a vector space V over a field F into itself and v ...