Introduction to Modern Algebra and Matrix Theory
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Title Preface Contents I. Affine Space; Linear Equations § 1. n-dimensional Affine Space § 2. Vectors § 3. The Concept of Linear Dependence § 4. Vector Spaces in Rn § 5. Linear Spaces § 6. Linear Equations II. Euclidean Space; Theory of Determinants § 7. Euclidean Length § 8. Volumes and Determinants § 9. The Principal Theorems of Determinant Theory § 10. Transformation of Coordinates § 11. Construction of Normal Orthogonal Systems and Applications § 12. Rigid Motions § 13. Affine Transformations III. Field Theory; The Fundamental Theorem of Algebra § 14. The Concept of a Field § 15. Polynomials over a Field § 16. The Field of Complex Numbers § 17. The Fundamental Theorem of Algebra IV. Elements of Group Theory § 18. The Concept of a Group § 19. Subgroups; Examples § 20. The Basis Theorem for Abelian Groups V. Linear Transformations and Matrices § 21. The Algebra of Linear Transformations § 22. Calculation with Matrices § 23. The Minimal Polynomial; Invariant Subspaces § 24. The Diagonal Form and its Applications § 25. The Elementary Divisors of a Polynomial Matrix § 26. The Normal Form Index
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