# 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:

One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.
—H.L. (Henry Lewis)