How to use Jordan normal form to determine $A^k?$
How the simplified way of the matrix $A$ on the Jordan normal form allows to determine easily this power?
2026-03-30 01:28:18.1774834098
How to determine the $A^k$ using Jordan normal form?
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$A = P J P^{-1}\\ A^k = P J^k P^{-1}$
What happens to a Jordan-normal matrix as you multiply it by itself?
The Jordan-normal matrix breaks down into blocks and each block is pretty regular in its behavior.