In this book, theorems as well as applied principles in linear algebra are described. Linear algebra holds a position of paramount importance in modern mathematics. Mathematicians have formulated highly effective methods for solving problems of this highly mature realm of mathematics. This book consists of selected topics in linear algebra, which represent the recent developments in the most widely encountered and discussed issues. It consists of various theorems and applications in different domains of linear algebra, such as linear systems, matrices, operators, inequalities, etc. It will prove to be a valuable source of information for researchers, scientists and graduate students.