Topics In Majorization, Dense Matrices And Their Linear Preservers

Here, we first review history and some applications of majorization with some kinds of linear preservers. Next, in chapter one we study classic majorization more precisely. In chapters two to six some recent kinds of majorizations have been introduced. In chapter seven we find the structure of multiplicative linear or strong linear preservers of some majorizations. Finally we study dense matrices and their linear preservers. So, I strongly recommend the enthusiasts in linear algebra and matrix analysis to read this book.