How to find jordan form given rank?

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SUMMARY

The discussion focuses on determining the Jordan form of an 8x8 matrix A with specific ranks: rank(A)=5, rank(A^2)=2, rank(A^3)=1, and rank(A^4)=0. It is established that the largest Jordan block is 4x4, with only one such block present due to the rank of A^3 being 1. The conversation emphasizes the relationship between the ranks of the matrix powers and the configuration of the Jordan blocks, particularly how the smaller blocks contribute to the overall rank.

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How to find jordan form given rank??

Find the jordan for of A given that A is an 8x8 matrix, rank(A)=5, rank(A^2)=2, rank(A^3)=1 and rank(A^4)=0.

I know that the largest jordan block will be 4x4 and there will be only one of them since the rank(A^3)=1 but how do i find the rest??
 
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well how do other blocks affect the total rank?
 

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