"This popular and successful text was originally written for a one-semester course in linear algebra at the sophomore undergraduate level. Students at this level generally have had little contact with complex numbers or abstract mathematics, so the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permit easy generalization to abstract vector spaces. The goal of the first two editions was the principal axis theorem for real symmetric linear transformation. The principal axis theorem becomes the first of two goals for this new edition, which follows a straight path to its solution."--BOOK JACKET.