A coordinate free book on linear and multilinear algebra defining determinants using exterior algebra

Question

I would like to find an advanced introduction to linear and multilinear algebra that is

1)Coordinate free

2)Use tensor products and exterior algebras to define determinants

3)DOES NOT assume a previous course in linear algebra, but only assumes some mathematical maturity and perhaps a little abstract algebra like group and field definitions and basic theorems.And definitely DOES NOT assume ANYTHING about determinants, so defines them from scratch.

Thanks in advance.

Answer 1

S.Winitzki "Linear Algebra via Exterior Products"