Matrix Inequalities and Their Extensions to Lie Groups gives a systematic and updated account of recent important extensions of classical matrix results, especially matrix inequalities, in the context of Lie groups. It is the first systematic work in the area and will appeal to linear algebraists and Lie group researchers.

Matrix Inequalities and Their Extensions to Lie Groups gives a systematic and updated account of recent important extensions of classical matrix results, especially matrix inequalities, in the context of Lie groups. It is the first systematic work in the area and will appeal to linear algebraists and Lie group researchers.

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.

This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades. The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations. In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed. In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed. The chapters give a comprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.

Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.

Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.