Matrix Positivity (Cambridge Tracts in Mathematics)

Johnson, Charles R./ Smith, Ronald L./ Tsatsomeros, Michael J.

Cambridge University Press（2020/10発売）

• 製本 Hardcover:ハードカバー版／ページ数 300 p.
• 言語 ENG
• 商品コード 9781108478717
• DDC分類 512.9434

Full Description

Matrix positivity is a central topic in matrix theory: properties that generalize the notion of positivity to matrices arose from a large variety of applications, and many have also taken on notable theoretical significance, either because they are natural or unifying. This is the first book to provide a comprehensive and up-to-date reference of important material on matrix positivity classes, their properties, and their relations. The matrix classes emphasized in this book include the classes of semipositive matrices, P-matrices, inverse M-matrices, and copositive matrices. This self-contained reference will be useful to a large variety of mathematicians, engineers, and social scientists, as well as graduate students. The generalizations of positivity and the connections observed provide a unique perspective, along with theoretical insight into applications and future challenges. Direct applications can be found in data analysis, differential equations, mathematical programming, computational complexity, models of the economy, population biology, dynamical systems and control theory.

Contents

Background; 1. Positivity classes; 2. Semipositive matrices; 3. P-matrices; 4. Inverse M-matrices; 5. Copositive matrices.