Introduction to Modern Algebra and Matrix Theory

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