Generalized Eigenvectors

Some articles on generalized eigenvectors, eigenvectors, eigenvector, generalized 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 ... 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
... 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 is an ordinary eigenvector ... In particular, (A - λI)n v = 0 for all generalized eigenvectors v associated with λ ...

Famous quotes containing the word generalized:

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