Books on coordinate transformations Which are the best books on linear algebra that explain in detail coordinate transformations (that math about matrices also used in computer graphics)?
 A: What you really want is a book on the symmetry relationship between linear transformations and classical geometry-there are a number of such books. A very good introduction to the geometry of linear algebra is Linear Algebra and Geometry: A Second Course by Irving Kaplansky. This is a strongly rigorous and abstract treatment by one of the masters of algebra of the last century. it focuses largely on the geometry of inner product and projective spaces,which are very naturally expressed in terms of linear transformations. And one of the most comprehensive treatments of the relationship between classical geometry and abstract algebra can be found in Groups and Symmetry by Paul Yale. This is a surprisingly sophisticated treatment of not only groups of transformations,but the relations between rings and algebras and the classical transformations as well. In the preface to the Dover edition,the author comments that one of the most important applications for the material in his book that has arisen since it was originally published is in computer graphics. I think you'll find this book very helpful indeed. The most important tool in computer graphics coordinates is the Householder matrix-which is discussed in any good book on numerical linear algebra. 
