TITLE: What is the connection between linear algebra and geometry?
QUESTION [10 upvotes]: I am currently studying linear algebra.
Yet, I found discussions about linear algebra usually explain things in a geometric fashion.
I am quite confused on how to link up these two topics.
Can anyone kindly recommend some books/readings for me as an introduction to the concept of combining these two topics?

REPLY [6 votes]: The classic introductions to the connection between linear algebra and classical geometry are Emil Artin's Geometric Algebra and Irving Kaplansky's Linear Algebra And Geometry. The latter now has a cheap Dover edition. 
But the best book on the subject is probably Thomas Banchoff and John Werner's Linear Algebra Through Geometry. The Banchoff/Werner book gives an entire course in linear algebra primarily in three-space where all concepts are given geometric interpretations, such as projection, inner product constructions and linear maps.It's extremely visual with lots of pictures.At the end of the book,abstract vector spaces are considered as generalizations of all that's gone before. I think you'll find that book to be exactly what you're looking for.