The book is even worse: "A vector, by contrast, is an ordered collection of numbers."

This is a terrible definition and makes talking about proper linear algebra proper impossible.

I tried to build intuition before going into the formal definitions.

Personally, I've always liked Bourbaki's books, but they're too formal for learning - especially in linear algebra, which I see as something meant for applications rather than pure math research.

Maybe I just oversimplified things or made them feel less "math".

here you go mate, exactly what you are looking for : https://github.com/little-book-of/linear-algebra#contributin...