This project aims to formalize basic results in linear algebra using the Lean proof assistant, loosely following the third edition of Axler's Linear Algebra Done Right. If you can, please contribute! Math is hard.
Exploit the typechecker---consider defining the image of a function as here. The alternative way is the set predicate ∃ x, y = f x. While both are equally valid, we would prefer the former since once the image_of's destructor is applied, the term y in question is unified with f x automatically. Whereas with the alternative definition, one would have to manually substitute y with f x using the given equality. Although the benefits aren't visible with such a small example, manual substitutions add up in larger proofs.
In general, we should structure definitions in a way that unifications that your average mathematician takes for granted when doing a proof are performed automatically. After all, we want to make the typechecker work for us---not the other way around.
Separation of concerns---TODO structuring sections for related definitions, namespaces, ...
Use structured proofs if possible---TODO for readability, especially if automation is doing magical things...
Naming conventions---TODO there is no right answer...
We should also the builtin projects & wiki features to track and document proofs, definitions, etc. with references to the textbook.