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2 Majorization theory.(MIMO Transceiver Design via Majorization Theory)
Foundations and Trends in Communications and Information Theory, December, 2006 by Jiang, Yi; Palomar, Daniel P.
Many of the problems addressed in this text result in complicated nonconvex constrained optimization problems that involve matrix-valued variables. Majorization theory is a key tool that allows us to transform these problems into simple problems with scalar variables that can be easily solved.
In this chapter, we introduce the basic notion of majorization and state some basic results. A complete and superb reference on the subject is the 1979 book by Marshall and Olkin [97]. (1) The 1997 book by Bhatia [15] contains significant material on majorization theory as well. Other textbooks on matrix and multivariate analysis may also include a section on majorization theory, e.g., [66, Sec. 4.3] (2) and [4, Sec. 8.10].
2.1 Basic Definitions
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