The book proves most things, just doesn't follow the standard math format of theorem-followed-by-proof. All the definitions are reasonably clear, and most of the proofs that are accessible and educational are given (e.g. the equivalence statements about invertible matrices). The exercises and problems also ask readers to complete several other interesting proofs (with solutions in the back).

In a future pass I plan to add more proofs, wherever adding formal structure doesn't interfere with the flow.