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Is there a good way of describing the form the inverse matrix of a "n by n matrix in Jordan canonical form"? I know how it should look like, but I don't know how to describe it... As an example: here.

Also, is there a simple way of getting the JCF of this inverse?

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    You can always find the Jordan form of a square matrix $A=V^{-1}JV$ and compute the inverse using the data given in the link. (assuming $A$ is invertible)2011-11-18
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    It's not clear to me what the first part of your question is asking. That may be partly due to the grammatical errors and ambiguities. Do you mean "the form *of* the inverse matrix"? And does "in Jordan canonical form" belong to "n by n matrix" or to "describing"?2011-11-18
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    Since Jordan blocks form the diagonal of the Jordan canonical forms and diagonal matrices behave nicely when taking powers, we need only investigate the problem for Jordan Blocks. The inverse of an upper triangular matrix is also upper triangular, and if $A$ has eigenvalues $\lambda_i $ then $A^{-1}$ has eigenvalues $ \lambda_i^{-1} . $ So we already know the diagonal of the upper triangular matrix which is the inverse of a Jordan block. Perhaps there is an easy way to find the other entries.2011-11-18
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    @percusse: Thanks, I know that we can find the JCF by $A=V^{-1}JV$. But I am looking for a way to describe the form of the inverse of a JCF matrix, something like "you take the reciprocal of the diagonal elements then if there is a 1 in the corner, you take -1/ab..." and so on but in a more concise /symbolic way...2011-11-18
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    @joriki: I have put in quote marks to group the words now. Sorry about the confusion.2011-11-18

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