LAII 007 Example of a Jordan normal form

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We will compute the Jordan normal form and the base change matrix for a matrix with one eigenvalue and one Jordan block.
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I dont understand how she find other eigenvectors, v2 and v3? It has to be only one eigenvector which correponds to v1. ?

felicityoswald
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A very nice explanation! I just want to point out a minor mistake in notation: The implication arrow in the three middle rows should face left since the v_i satisfy the left equation, but are to determined by it.

Pfandleiher
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I have a question ..for v3 could it be also {1, 0, 1} ?

mihaipreda