Linear Algebra: From the Beginning
Eric A. Carlen, Maria C. Carvalho
Reflects the ways computers have changed the course. Having computers to do the number-crunching opens up a number of ways to solve all but the simplest linear algebra problems. This text provides more thorough explanations of the subject’s fundamental ideas and of the capabilities of various software packages, to help students choose the best way to solve a problem.
Careful introduction of abstraction. The first two chapters (Vectors, Matrices, and Linear Transformations; and The Solution Set of a Linear System) are designed to help students make the transition from concrete to abstract algebraic thinking, preparing them for learning how and when to use a greater variety of problem-solving methods.
Full proofs with every theorem help students achieve a basic level of “mathematical maturity” realm at this introductory stage. Concise yet accurate proofs, as well as interesting examples, accompany every theorem.
Overview sections begin each chapter and provide students with a clear sense of the scope and relevance of the chapter, making connections to other chapters in the text so students see where the material fits in the overall course.
Table of Contents
1.Vectors, Matrices, and Linear Transformations
2. The Solution Set of a Linear System
3. The Image of Linear Transformation
5. The Eigenvalue Problem
6. More About Eigenvectors and Eigenvalues
7. Abstract Vector Spaces