[Merged by Bors] - feat(linear_algebra/nonsingular_inverse): state Cramer's rule explicitly #4700
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Mostly so that we can add an entry to the Freek 100.
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I feel this is cleaner, though it's obviously a subjective call.
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…ow`. This really just moves a transpose operation from the definition of `cramer_map` to the definition of `adjugate`. I claim the new definitions have the slight advantage of being more conventional. In the course of doing this I noticed that there still seem to be a few places where the words 'row' and 'column' are backwards. I fixed the instances that I encountered but did not attempt an exhaustive search.
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Co-authored-by: Johan Commelin <johan@commelin.net>
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…tly (#4700) Mostly so that we can add an entry to the Freek 100. Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
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Mostly so that we can add an entry to the Freek 100.
Note that we state this using the slightly low-level
matrix.mul_vecinstead of building on top ofmatrix.to_lin'. This is partly because the current status of the import hierarchy (matrix.to_lin'is defined in a file importingnonsingular_inverse.lean) and partly because the statement in terms ofto_lin'turns out to need additional ascriptions which, IMHO, render the statement ofcramers_ruleeven less readable to the casual reader arriving from the Freek list.Notwithstanding the above, I am more than happy to be persuaded to do things differently!