Group Majorization Methods Extensions of Matrix Inequalities to Lie Groups

This edited book, On Group Majorization Methods and Extensions of Matrix Inequalities to Lie Group, is a collection of contemporary open access articles that highlight various aspects of majorization methods and the latest extensions of matrix inequalities. The book consists of two parts, one focuses on the refinement and expansion of matrix inequalities derived from the theorem of majorization; the other focuses on the study of inequalities in the context of Heisenberg and Lie groups. Part I, chapters 1 to 10 feature the following research topics: Generalization of the weighted majorization theorem; Extensions of majorization inqualities to convex and invex functions; Refinements of upper and lower bounds for several important inequalities such as the Sherman's the Jensen's, the Fischer's, the Hadamard's and the Lieb-Thirring inequalities, The connection between Shannon entropy with the theory of majorization; Multivariate trace inequalities that can extend the Golden-Thompson and the Araki-Lieb-Thirring inequalities. Part II, Chapters 11 to 15 feature inequalities such as the Hardy's, Weighted Rellich and Sobolev-Rellich inequalities in the context of nilpotent Lie groups. The intended audience of this edited book will mainly consist of graduate students and researching academics who are focused on various fields of mathematical sciences. The content of this volume will be of particular interest to linear algebraists and Lie group theoreticians. It is suitable for readers who possess an advanced university-level knowledge within the applicable fields of algebra, calculus, geometry, quantum mechanics, group theory or complex analysis. Book jacket.