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

Generalized Eigenvector - For Defective Matrices

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**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

... 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)