The present book is intended for the advanced level undergraduate, and postgraduate students, in mathematics and other disciplines, who need a comprehensive knowledge of linear algebra. It can also be a reference source for teachers, looking for detailed proofs of results, given in elementary books, without proofs. The linear algebra is developed over a field. The first chapters are devoted to basic concepts of matrices, abstract vector spaces, linear transformations and determinants. The other three chapters discuss various canonical forms of matrices, inner product spaces, sesquilinear forms, and bilinear forms. The book contains detailed proofs of various results; these proofs may or may not be discussed by a teacher, depending upon the course being offered. The further elucidate the material in the book, a large number of examples and remarks are given.About the AuthorDR. SURJIT SINGH studied in the Delhi University for his degrees of B.Sc (Hons.), M.Sc and Ph.D. He was awarded Ph.D in 1969. He started his teaching carerrer as a Lecturer in Mathematics at the Kirori Mal College in 1964. In 1969, he joined the Aligarh Muslim University, and in 1975, the Guru Nanak Dev University, Amritsar, as a Professor and Head of the Department of Mathematics. He left the Guru Nanak Dev University, in 1979, for Kuwait, where he has been working as a Professor of Mathematics at the Kuwait University since then. The main area of his research interest is the Theory of Rings and Modules (Algebra). He has more than seventy research papers on various topics in the Theory of Rings and Modules, published in internationally famous journals. He has supervised a large number of students for Ph.D, and is a co-author of a book on Modern Algebra, published by Vikas Publishing House. He has held a number of visiting appointments at universities in USA and Canada.Table of Contents Algebra And Matrices, Vector Spaces, Linear Transformations, Determinants, Single Linear operator, Single Linear

Algebra and metrics, Vector Spaces, Linear Transformations, etc.