generalized eigenvector

Jeremy Watts · science forum Guru Wannabe Joined: 24 Mar 2005 Posts: 239

the definition of a generalized eigenvector (not the same generalized
eigenvector of the generalized eigenvalue problem), is according to
'Schaum's Outlines' :-

A vector Xm is a generalized vector if :-

(A - lambdaI)^m Xm = 0

but,

(A - lambdaI)^(m-1) Xm =/= 0

where Xm is an eigenvector of rank 'm', 'A' is a square matrix and 'lambda'
an associated eigenvalue.

But according to wikipedia, the definition is simply :-

http://en.wikipedia.org/wiki/Generalized_eigenvector

why do these definitions differ??

G.E. Ivey · science forum Guru Joined: 29 Apr 2005 Posts: 308

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