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

Ilse C. F. Ipsen is Professor of Mathematics at North Carolina State University. She is the SIAM Vice President for Programs and section editor of the Problems and Techniques section of SIAM Review. She is also a member of the editorial boards of the SIAM Journal on Matrix Analysis and Applications, Numerische Mathematik, and Numerical Linear Algebra with Applications.

Preface; Introduction; 1 Matrices; 2 Sensitivity, Errors, and Norms; 3 Linear Systems; 4 Singular Value Decomposition; 5 Least Squares Problems; 6 Subspaces; Index