Matrix Inequalities and Their Extensions to Lie Groups

Tin-Yau Tam currently serves as the Chair and Professor of the Department of Mathematics and Statistics at Auburn University. He was honored as Lloyd and Sandra Nix Endowed Professor (2012–2015). He has served as Director of Assessment and Planning (2000–2012) and Special Assistant to the Provost (2008–2009). He has served as a member of the board of directors of the International Linear Algebra Society (2009–2013). Tam’s areas of specialization are Matrix Theory and their Applications, Multilinear Algebra, and Lie Theory. He is the Editor-in-Chief of the Alabama Journal of Mathematics. He serves on the editorial boards of Linear and Multilinear Algebra, Electronic Linear Algebra, Special Matrices, and Proyecciones, Revista de Matemática. Xuhua Liu is an Assistant Professor of Mathematics at North Greenville University. He earned a PhD in Mathematics from Auburn University under the guidance of Professor Tin-Yau Tam in August 2012. His research interests include Matrix Theory and Lie Theory.

Preface. Review of Matrix Theory. Structure Theory of Semisimple Lie Groups. Inequalities for Matrix Exponentials. Inequalities for Spectral Norm. Inequalities for Unitarily Invariant Norm. Inequalities for Geometric Means. Kostant Convexity Theorems.