Linear Algebra Thoroughly Explained

Milan Vujicic was Professor of Theoretical Physics at the University of Belgrade and the book is based on lectures he gave there to both undergraduate and postgraduate students over a period of several decades. He also lectured on the applications of linear algebra in particle physics at the University of Adelaide and, after retirement, taught the subject at the most basic level to Teaching Diploma students at the University of Malta. It was his success in this most recent endeavour that inspired him to write this book which sets out to explain Linear Algebra from its fundamentals to the most advanced level where he, himself, used it throughout his career to solve problems involving linear and anti-linear correlations and symmetries in quantum mechanical applications. Linear Algebra is one of the most important topics in mathematics, of interest in its own right to mathematicians, but also as an enormously powerful tool in the applied sciences, particularly in physics and engineering. A special feature of this book is its didactical approach, with a myriad of thoroughly worked examples and excellent illustrations, which allows the reader to approach the subject from any level and to proceed to that of the most advanced applications. Throughout, the subject is taught with painstaking care. The author of this book was Professor of Theoretical Physics at the University of Belgrade. The book is based on lectures he gave there to both undergraduate and postgraduate students over a period of several decades. It sets out to explain Linear Algebra from its fundamentals to the most advanced level. A special feature of this book is its didactical approach, with a myriad of thoroughly worked examples and excellent illustrations, which allows the reader to approach the subject from any level and to proceed to that of the most advanced applications. Throughout, the subject is explained with painstaking care. "Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and inclusive presentation of the basic theory is illustrated throughout with an abundance of worked examples." "The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a general resource book for the subject."--Jacket Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject front-matter......Page 1 01Vector Spaces......Page 11 02Linear Mappings and Linear Systems......Page 68 03Inner-Product Vector Spaces (Euclidean and Unitary Spaces)......Page 128 04Dual Spaces and the Change of Basis......Page 154 05The Eigen Problem or Diagonal Form of Representing Matrices......Page 181 06Tensor Product of Unitary Spaces......Page 251 07Dualism between Unitary Spaces (Sect. 4.1) and Isodualism between Their Superspaces (Sect. 4.7)......Page 270 back-matter......Page 285