This book investigates the mathematical concept of total positivity and its diverse applications across various fields. It delves into the theoretical underpinnings of totally positive matrices and functions, exploring their properties and characterizations. The work then extends these concepts to areas such as approximation theory, numerical analysis, and probability, demonstrating their utility in solving complex problems.

This work is recognized as a comprehensive and rigorous treatment of total positivity, suitable for researchers and advanced students in mathematics. Its detailed exploration of theoretical aspects and broad range of applications positions it as a valuable reference in fields ranging from pure mathematics to applied sciences. The book is noted for its depth and the clarity with which complex concepts are presented.