This book describes basic methods and algorithms used in modern, real problems likely to be encountered by engineers and scientists - and fosters an understanding of why mathematical techniques work and how they can be derived from first principles.Assumes no previous exposure to linear algebra. Presents applications hand in hand with theory, leading readers through the reasoning that leads to the important results. Provides theorems and proofs where needed. Features abundant exercises after almost every subsection, in a wide range of difficulty.A thorough reference for engineers and scientists.