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Mo-ers,

Do you know how it was that the study of the Jordan canonical form began?

There are certain things that may be said once one has thought about the matter: for instance, one can say that the consideration of the Jordan canonical form of a matrix $A \in \mathbf{M}_{n \times n}(\mathbb{C})$ is valuable 'cause it facilitates certain commonplace computations related to $A$ (its powers, its exponential, etc.).

Do we know if the individual that first introduced the form in the mathematical realm (Camille Jordan? Wilhelm Jordan?) was somewhat motivated by this sort of things? Would you be so kind as to suggest a text in which one can find a very concrete, down-to-earth, and down to the nitty-gritty explanation of why the mathematician that "invented/discovered" the form did it?

On a lighter note, what's in your Weltanschauung the book on algebra (or rather linear algebra) that a person interested in mastering the Jordan canonical form should definitely peruse?

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    $\begingroup$ Much more than the computational aspect, my perspective from the modern day on the significance of the Jordan canonical form is that it provides a set of representatives for the conjugacy classes of matrices over algebraically closed fields. I don't know if that motivated Jordan, though. $\endgroup$
    – LSpice
    May 29, 2019 at 21:36
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    $\begingroup$ See also hsm.stackexchange.com/questions/5230/… . $\endgroup$
    – LSpice
    May 29, 2019 at 21:38
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    $\begingroup$ I don’t know the actual history, but if you try to diagonalize a matrix and fail then you will invent Jordan normal form. $\endgroup$ May 29, 2019 at 22:38
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    $\begingroup$ @AlexandreEremenko: [citation needed]... $\endgroup$
    – Jamai-Con
    May 30, 2019 at 0:03
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    $\begingroup$ I responded off the cuff because I love the Jordan canonical form and wanted to opine on it; but, on further reflection, I think that this belongs better on a site devoted to historical questions, like HSM. $\endgroup$
    – LSpice
    May 30, 2019 at 0:20

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