[Koshkin]

> No

Gilbert Strang (already mentioned by fellow commenters).

> The subject is too young

"The first modern and more precise definition of a vector space was introduced by Peano in 1888; by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged." (from Wikipedia)

[resource0x]

The first book was written in 1942 - it's mentioned explicitly in LADR. It doesn't mean the concepts didn't exist - they did, Frobenius even built a brilliant theory around them (representation theory), but the subject was defined quite loosely - apparently no one cared to collect the results in one place. It doesn't even matter much: I remember taking the course in 1974, and it was totally different from what is being taught today.