This textbook provides a full treatment of Linear Algebra devoted to undergraduate and graduate physics students. Although the mathematical level is similar to the corresponding mathematical textbooks in regard to definitions, propositions and proofs, it adopts a language and approach more attuned to the reader’s familiarity with physics lectures and physics textbooks. A distinctive feature is the emphasis placed on the significance of bases within a vector space. As a result, students gain a deeper understanding of how vector indices, despite their abundance, serve not as enemies but as friends since they give additional information about the mathematical objects being used, and facilitate access to tensor formalism.

The book offers numerous worked examples and exercises with solution hints to deepen this knowledge

Table of Contents

1. The Role of Group Action

2. A Fresh Look at Vector Spaces

3. The Role of Bases

4. Spacetime and Linear Algebra

5. The Role of Matrices

6. The Role of Dual Spaces

7. The Role of Determinants

8. First Look at Tensors

9. The Role of Eigenvalues and Eigenvectors

10. Operators on Inner Product Spaces

11. Positive Operators-Isometries-Real Inner Product Spaces

12. Applications

13. Duality

14. Tensor Formalism

About the Author

Nikolaos A. Papadopoulos, professor emeritus at University of Mainz, Germany. 1978 Ph.D. in Theoretical Physics at ETH Zurich. Habilitation 1985 at University of Mainz. 1985-2014 senior lecturer/professor at University of Mainz. After his retirement in 2014 continuing activities as lecturer and researcher at the University of Mainz.

Florian A. Scheck, (1936-2024) professor emeritus at University of Mainz, Germany. Born in 1936, diploma degree 1962 , Ph.D. (Dr. rer.nat) 1964, both at U. Freiburg, Germany. Habilitation at U. Heidelberg 1968. Guest scientist at the Weizmann Institute of Science, Rehovoth, (1964 – 1966), research assistant U. Heidelberg, (1966 – 1968), research fellow at CERN, Geneva, (1968 – 1970), head of theory group SIN/PSI, lecturer and titular professor at ETH Zurich (1970 – 1976). Professor of theoretical Physics U. Mainz (1976 – 2005). Numerous visits as guest scientistor guest professor, Helsinki, Montpellier, Marseille, San José (Costa Rica), Bogota (Columbia).