L. Shen & Haohao Wang 
Linear Algebra [PDF ebook] 

The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. The book is suitable for a one semester coursein linear algebra that can be used in a variety of contexts. The presentationof the material combines definitions and proofs with an emphasis oncomputational applications, providing examples that illustrate the use ofsoftware packages such as
Mathematica®,
Maple®, and Sage.
Features:
– Introduces the fundamental concepts of linear algebra and applies the theorems in computation-oriented applications
– Presents a brief introduction of some aspects of abstract algebra that relate directly to linear algebra, such as groups, rings, modules, fields and polynomials over fields.