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Book Synopsis

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.

Linear Algebra

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    A Paperback by Jörg Liesen

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      Book details

      Publisher Springer Nature
      Published 29 July 2025
      ISBN-13 9783031932595
      978-3031932595
      ISBN-10 3031932595
      Also in:
      Algebra

      Description

      Book Synopsis

      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.

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