generalized eigenvector - Wolfram|Alpha

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Input interpretation

generalized eigenvector

Definition

A generalized eigenvector for an n×n matrix A is a vector v for which
(A - λ I)^k v = 0
for some positive integer k element Z^+. Here, I denotes the n×n identity matrix. The smallest such k is known as the generalized eigenvector order of the generalized eigenvector. In this case, the value λ is the generalized eigenvalue to which v is associated and the linear span of all generalized eigenvectors associated to some generalized eigenvalue λ is known as the generalized eigenspace for λ.

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Related terms

diagonalizable matrix | eigenspace | eigenvalue | eigenvector | linearly independent | matrix | vector basis

Subject classifications

MathWorld

matrix eigenvalues

MSC 2010

15A18 | 65F15

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