Linear Algebra – Jörg Liesen, Volker Mehrmann – 1st Edition


This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations.

The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments.

Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.

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  • Chapter 1. Linear algebra in every day life.
    Chapter 2. Basic mathematical concepts.
    Chapter 3. Algebraic structures.
    Chapter 4. Matrices.
    Chapter 5. The chelon form and the rank of matrices.
    Chapter 6. Linear systems of equations.
    Chapter 7. Determinants of matrices.
    Chapter 8. The characteristic polynomial and eigenvalues of matrices.
    Chapter 9. Vector spaces.
    Chapter 10. Linear maps.
    Chapter 11. Linear forms and bilinear forms.
    Chapter 12. Euclidean and unitary vector spaces.
    Chapter 13. Adjoints of linear maps.
    Chapter 14. Eigenvalues of endomorphisms.
    Chapter 15. Polynomials and the fundamental theorem of algebra.
    Chapter 16. Cyclic subspaces, duality and the Jordan canonical form.
    Chapter 17. Matrix functions and systems of differential equations.
    Chapter 18. Special classes of endomorphisms.
    Chapter 19. The singular value decomposition.
    Chapter 20. The Kronecker product and linear matrix equations.
  • Citation

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