Linear Algebra / by Jörg Liesen, Volker Mehrmann.

Format:

Book

Author/Creator:

Liesen, Jörg, Author.

Mehrmann, Volker., Author.

Series:

Springer Undergraduate Mathematics Series, 2197-4144

Language:

English

Subjects (All):

Algebras, Linear.

Linear Algebra.

Local Subjects:

Linear Algebra.

Physical Description:

1 online resource (XV, 389 p. 25 illus.)

Edition:

2nd ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This self-contained textbook, now in a thoroughly revised and expanded second edition, takes a matrix-oriented approach to Linear Algebra. It presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its derivation. Throughout, the book emphasizes the practical applicability of results. It therefore also covers special topics in Applied Linear Algebra, such as matrix functions, the singular value decomposition, the Kronecker product, and linear matrix equations. New to this edition are topics such as the Frobenius canonical form and a more detailed treatment of infinite-dimensional vector spaces, along with many additional exercises. The book’s matrix-oriented approach enhances intuition and simplifies abstract concepts, making them easier to understand and to apply in real-world scenarios. Key applications are illustrated through detailed examples. Additionally, several "MATLAB Minutes" allow students to explore concepts and results through computational experiments, supported by a brief introduction to MATLAB fundamentals. Together with over 380 exercises, this encourages active engagement with the material.

Contents:

Chapter 1. Linear Algebra in every day life

Chapter 2. Basic mathematical concepts

Chapter 3. Algebraic structures

Chapter 4. Matrices

Chapter 5. The echelon 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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-93260-9

OCLC:

1535979488