This self-contained textbook presents matrix analysis in the context of numerical computation with numerical conditioning of problems and numerical stability of algorithms at the forefront. Using a unique combination of numerical insight and mathematical rigor, it advances readersÕ understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. 

This book differs from other numerical linear algebra texts by offering

• a systematic development of numerical conditioning,
• a simplified concept of numerical stability in exact arithmetic,
• simple derivations,
• a high-level view of algorithms, and
• results for complex matrices.

The material is presented at a basic level, emphasizing ideas and intuition, and each chapter offers simple exercises for use in the classroom and more challenging exercises for student practice.

This book is intended for first-year graduate students in engineering, operations research, computational science, and all areas of mathematics. It also is appropriate for self-study.

Keywords:  numerical conditioning, sensitivity, numerical stability, singular value decomposition