Timeline for Order of column vectors in jordan normal form

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Dec 4, 2012 at 9:53	comment	added	lysgaard		Thanks. This means that the $lambdas$ in the $J$ matrix corresponding to a generalized eigenvector should have a 1 over them? (if i follow wikipedias example.) What if there are several general eigenvectors in the block? Does the order of them matter or is the only important thing that the eigenvector appear before the generalized eigenvectors.
Dec 3, 2012 at 19:56	comment	added	Arturo Magidin		It depends on whether you like your Jordan blocks to have the 1s above the diagonal or below the diagonal. The two forms are similar, though. They should appear in $P$ in whatever order you choose for your ordered basis. In the example in Wikipedia, $x$ is a generalized eigenvector but not an eigenvector, and $y=(A-4I)x$ is an eigenvector. Since in the Jordan form the eigenvector occurs before the generalized eigenvector (the third column corresponds to an eigenvector, but the fourth column does not), then the eigenvector occurs first in $P^{-1}$ (following your ntoation, not Wikipedia's)
Dec 3, 2012 at 19:52	history	asked	lysgaard	CC BY-SA 3.0