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My professor said that the main idea of finding a Jordan normal form is to find the closest 'diagonal' matrix that is similar to a given matrix that does not have a similar matrix that is diagonal. I know that using a diagonal matrix is good for computations and simplifying powers of matrices. But what is the potential of finding a matrix with Jordan form? what is this 'almost diagonal' matrix gives me? We learnt how to find it, without knowing what is the main idea behind it and what are the applications used with it, so I can't really understand it.