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. 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.

Vector Spaces.- Linear Mappings and Linear Systems.- Inner-Product Vector Spaces (Euclidean and Unitary Spaces).- Dual Spaces and the Change of Basis.- The Eigen Problem or Diagonal Form of Representing Matrices.- Tensor Product of Unitary Spaces.- The Dirac Notation in Quantum Mechanics: Dualism between Unitary Spaces (Sect. 4.1) and Isodualism between Their Superspaces (Sect. 4.7).

From the reviews:

"It is based on lectures by the author ... to both undergraduate and graduate students in Europe over a period of several decades. ... it does have some parts that are appropriate for undergraduates and others seem to be intended for more advanced students. ... Examples throughout the book are geared toward quantum theory, and unitary and Hermitian matrices are treated thoroughly. ... students whose specific objective is to prepare for the study of quantum mechanics will find it useful for self-study." (David S. Watkins, SIAM Review, Vol. 51 (3), 2009)