Linear Algebra Through Geometry

"Linear Algebra Through Geometry" introduces the concepts of linear algebra through the study of two- and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices and quadratic forms. The final chapter deals with applications of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only basic required knowledge for using this book (with the exception of one section on systems of differential equations) is a working knowledge of school geometry, algebra and introductory trigonometry.