Author | Curtis, Charles W. author |
---|---|
Title | Linear Algebra [electronic resource] : An Introductory Approach / by Charles W. Curtis |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1984 |
Edition | 4 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1136-5 |
Descript | X, 350 p. online resource |
1. Introduction to Linear Algebra -- 1. Some problems which lead to linear algebra -- 2. Number systems and mathematical induction -- 2. Vector Spaces and Systems of Linear Equations -- 3. Vector spaces -- 4. Subspaces and linear dependence -- 5. The concepts of basis and dimension -- 6. Row equivalence of matrices -- 7. Some general theorems about finitely generated vector spaces -- 8. Systems of linear equations -- 9. Systems of homogeneous equations -- 10. Linear manifolds -- 3. Linear Transformations and Matrices -- 11. Linear transformations -- 12. Addition and multiplication of matrices -- 13. Linear transformations and matrices -- 4. Vector Spaces with an Inner Product -- 14. The concept of symmetry -- 15. Inner products -- 5. Determinants -- 16. Definition of determinants -- 17. Existence and uniqueness of determinants -- 18. The multiplication theorem for determinants -- 19. Further properties of determinants -- 6. Polynomials and Complex Numbers -- 20. Polynomials -- 21. Complex numbers -- 7. The Theory of a Single Linear Transformation -- 22. Basic concepts -- 23. Invariant subspaces -- 24. The triangular form theorem -- 25. The rational and Jordan canonical forms -- 8. Dual Vector Spaces and Multilinear Algebra -- 26. Quotient spaces and dual vector spaces -- 27. Bilinear forms and duality -- 28. Direct sums and tensor products -- 29. A proof of the elementary divisor theorem -- 9. Orthogonal and Unitary Transformations -- 30. The structure of orthogonal transformations -- 31. The principal axis theorem -- 32. Unitary transformations and the spectral theorem -- 10. Some Applications of Linear Algebra -- 33. Finite symmetry groups in three dimensions -- 34. Application to differential equations -- 35. Analytic methods in matrix theory -- 36. Sums of squares and Hurwitzโs theorem -- Bibliography (with Notes) -- Solutions of Selected Exercises -- Symbols (Including Greek Letters)