The Complex Gradient Operator and the CR-Calculus

Details The Complex Gradient Operator and the CR-Calculus The Complex Gradient Operator and the CR-Calculus

2009-06-26

arxiv.org/abs/0906.4835v1

Mathematics

Optimization and Control

Scientific paper

A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus. The presented material is suitable for exposition in an introductory Electrical Engineering graduate level course on the use of complex gradients and complex Hessian matrices, and has been successfully used in teaching at UC San Diego. Going beyond the commonly encountered treatments of the first-order complex vector calculus, second-order considerations are examined in some detail filling a gap in the pedagogic literature.

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