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Who studied invertible linear transformations for the first time? I would guess these linear transformations weren't studied for the sake of studying invertible linear transformations, they probably were studied and developed as a helping tool for understanding other topics

What are some related references?

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    $\begingroup$ Basic linear algebra relates invertibililty of a linear transformation to the fact that a system of linear equations has a unique solution (as opposed to none, or infinitely many). Certainly people talked about this long before the notion of linear transformation was formalized. $\endgroup$ Commented Jul 11 at 21:32

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