Linear Algebra Through Geometry (Undergraduate Texts in Mathematics)

By Thomas F. Banchoff, John Wermer, Thomas Banchoff

Book Overview

Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful 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 treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry.

• Format: Paperback
• Language: English
• ISBN: 1461287529
• ISBN13: 9781461287520
• Release Date: March 2012
• Publisher: Springer
• Length: 308 Pages
• Weight: 0.90 lbs.
• Dimensions: 0.7" x 6.1" x 9.2"

Customer Reviews

A wonderful introduction

A crystal clear book. It shows the geometrical significance of topics like eigenvalues/eigenvectors without losing the intuition in the formalism, like so many other books on Linear Algebra. The book would be particularly suitable for scientists, though prospective mathematicians would appreciate the "whys" too. I only wish there were follow-on, more advanced, volumes!