TITLE: A coordinate free book on linear and multilinear algebra defining determinants using exterior algebra
QUESTION [6 upvotes]: 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.

REPLY [3 votes]: S.Winitzki "Linear Algebra via Exterior Products"