'This book addresses the problem of complex-valued derivatives in a wide range of contexts. The mathematical presentation is rigorous but its structured and comprehensive presentation makes the information easily accessible. Clearly, it is an invaluable reference to researchers, professionals and students dealing with functions of complex-valued matrices that arise frequently in many different areas. Throughout the book the examples and exercises help the reader learn how to apply the results presented in the propositions, lemmas and theorems. In conclusion, this book provides a well organized, easy to read, authoritative and unique presentation that everyone looking to exploit complex functions should have available in their own shelves and libraries.' Professor Paulo S. R. Diniz, Federal University of Rio de Janeiro (UFRJ)

'Complex vector and matrix optimization problems are often encountered by researchers in the electrical engineering fields and much beyond. Their solution, which can sometimes be reached from using existing standard algebra literature, may however be a time consuming and sometimes difficult process. This is particularly so when complicated cost function and constraint expressions arise. This book brings together several mathematical theories in a novel manner to offer a beautifully unified and systematic methodology for approaching such problems. It will no doubt be a great companion to many researchers and engineers alike.' Professor David Gesbert, EURECOM, Sophia-Antipolis, France

'… an excellent monograph … The book is suitable as a textbook in graduate-level studies and research.' Zentralblatt MATH