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Description of  Jacobians of matrix transformations and functions of matrix arguments

This book concentrates on the topic of evaluation of Jacobians in some specific linear as well as nonlinear matrix transformations, in the real and complex cases, which are widely applied in the statistical, physical, engineering, biological and social sciences. It aims to develop some techniques systematically so that anyone with a little exposure to multivariable calculus can easily follow the steps and understand the various methods by which the Jacobians in complicated matrix transformations are evaluated. The material is developed slowly, with many worked examples, aimed at self-study. Some exercises are also given at the end of each section. The book is a valuable reference for statisticians, engineers, physicists, econometricians, and applied mathematicians. It can be used for a one-term graduate level course on Jacobians and functions of matrix argument