Harold Edwards gave a presentation on this topic at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida. The talk he gave was a brief introduction to his new book, entitled Linear Algebra. A summary of this book is available from Birkhauser, the publisher. Edwards writes:

I believe that the approach to linear algebra that I develop in my book is worthy of the consideration of math educators and deserves to be adopted at a wide range of schools.