eigenvector
Let be an square matrix and an column vector. Then a (right) eigenvector of is a nonzero vector such that
for some scalar , i.e. such that the image of under the transformation is a scalar of . One can similarly define left eigenvectors in the case that acts on the right.
One can find eigenvectors by first finding eigenvalues, then for each eigenvalue , solving the system
to find a form which characterizes the eigenvector (any of is also an eigenvector). Of course, this is not necessarily the best way to do it; for this, see singular value decomposition.
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 |