Description
Book SynopsisThe Essentials of a First Linear Algebra Course and More
Linear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.
An Engaging Treatment of the Interplay among Algebra, Geometry, and Mappings
The text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra, including linear systems, vector geometry, matrix algebra, subspaces, independence, dimension, orthogonality, eigenvectors, and diagonalization.
A Smooth Transition to the Conceptual Realm of Higher Mathematics
This book guides students on a journey from
Trade Review
"All the standard topics of a first course are covered, but the treatment omits abstract vector spaces. … What is unusual is the author's aim to interpret every concept and result geometrically, thus motivating the student to learn to visualize what is going on, rather than just relying on calculations. This is a strong and useful feature. … The book has very many practice sections with over 500 exercises, most of them numerical. … As the author mentions in the preface, it was his aim to provide a sound mathematical introduction, and in the reviewer's opinion he has succeeded in doing this."
—Zentralblatt MATH 1314
Table of ContentsVectors, Mappings, and Linearity. Solving Linear Systems. Linear Geometry. The Algebra of Matrices. Subspaces. Orthogonality. Linear Transformation. Appendices. Index.
