Let A be an n×n square matrixMathworldPlanetmath and x an n×1 column vectorMathworldPlanetmath. Then a (right) eigenvectorMathworldPlanetmathPlanetmathPlanetmath of A is a nonzero vector x such that


for some scalar λ, i.e. such that the image of x under the transformation A is a scalar of x. One can similarly define left eigenvectors in the case that A acts on the right.

One can find eigenvectors by first finding eigenvalues, then for each eigenvalueMathworldPlanetmathPlanetmathPlanetmathPlanetmath λi, solving the system


to find a form which characterizes the eigenvector xi (any of xi is also an eigenvector). Of course, this is not necessarily the best way to do it; for this, see singular value decompositionMathworldPlanetmath.

Title eigenvector
Canonical name Eigenvector
Date of creation 2013-03-22 12:11:55
Last modified on 2013-03-22 12:11:55
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 12
Author mathcam (2727)
Entry type Definition
Classification msc 65F15
Classification msc 65-00
Classification msc 15A18
Classification msc 15-00
Related topic SingularValueDecomposition
Related topic Eigenvalue
Related topic EigenvalueProblem
Related topic SimilarMatrix
Related topic DiagonalizationLinearAlgebra
Defines scalar multiple