Linear algebra is a relatively new area of Mathematics, whose concepts were formulated starting in the late nineteenth century. A few of the common topics one normally encounters in linear algebra are vectors, matrices and linear maps. These areas of study have wide ranging applications in physics, the natural and social sciences, and serve as a stepping stone for studying nonlinear systems that are constructed to model real world phenomena.
‘Principles of Linear Algebra with Maple’ is an attempt to cross the gap between beginning linear algebra and the computational and geometrical linear algebra one encounters more frequently in applied settings. Many topics in linear algebra are quite simple, but can be computationally intensive. Computer algebra systems, such as Maple, are important in that they can be used to apply simple concepts to computationally challenging problems. Furthermore, the graphical abilities of Maple help to visualize many of the geometric aspects of linear algebra. The book itself is a self-contained first course in the subject areas already mentioned as well as many others. Additionally, topics such as: sensitivity of solutions to errors in systems of equations and rotations of geometric objects in the plane and in space, can only be covered with the use of a computer algebra system.
An attempt is also made to use the full power of Maple: graphics in two and three dimensions, animations, symbolic manipulations, numerical computations and programming, to name just a few. In the text, we include all of the Maple commands required to solve complex and computationally challenging linear algebra problems.
This is not just a theory-proof-problem text; we explore topics in a very reader friendly and natural way. Our approach to presenting the material has made the text very readable, and has made the use of Maple to solve problems fun and less tedious. All of these facts make this book current, useful and interesting beyond the standard scope of a linear algebra text, while still giving the reader an understanding of the underlying fundamental concepts that make up the field of linear algebra.
We hope that students and educators alike will take the time to utilize Maple in their explorations of the various topics covered in this text.