Generalized Eigenvectors

Some articles on generalized eigenvectors, eigenvectors, generalized eigenvector, eigenvector:

Generalized Eigenvector - For Defective Matrices
... Generalized eigenvectors are needed to form a complete basis of a defective matrix, which is a matrix in which there are fewer linearly independent eigenvectors than eigenvalues (counting ... Over an algebraically closed field, the generalized eigenvectors do allow choosing a complete basis, as follows from the Jordan form of a matrix ... λ of a matrix A has an algebraic multiplicity m but fewer corresponding eigenvectors ...
Eigenvalue Algorithm - Eigenvalues and Eigenvectors
... numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation where v is a nonzero n × 1 column vector, I is ... When k = 1, the vector is called simply an eigenvector, and the pair is called an eigenpair ... Any eigenvalue λ of A has ordinary eigenvectors associated to it, for if k is the smallest integer such that (A - λI)k v = 0 for a generalized eigenvector v, then (A - λI)k-1 v ...

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