Jordan form step by step general algorithm

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So I am trying to compile a summary of the procedure one should follow to find the Jordan basis and the Jordan form of a matrix, and I am on the lookout for free resources online where the algorithm to be followed is clearly explained in an amenable way.

I have found some interesting youtube videos but what I am on the lookout for is a written thing.

Alternatively, if you are so kind as to flesh out the procedure I would be happy to accept that as an answer.