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0 reviews(Ebook) Introduction to Modern Algebra and Matrix Theory 2nd Edition by Otto Schreier, Emanuel Sperner - Ebook PDF Instant Download/Delivery: 9780486482200 ,0486482200
Full download (Ebook) Introduction to Modern Algebra and Matrix Theory 2nd Edition after payment
Product details:
ISBN 10: 0486482200
ISBN 13: 9780486482200
Author: Otto Schreier, Emanuel Sperner
(Ebook) Introduction to Modern Algebra and Matrix Theory 2nd Edition Table of contents:
Chapter 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
Homogeneous Linear Equations
Non-homogeneous Linear Equations
Geometric Applications
Chapter II EUCLIDEAN SPACE; THEORY OF DETERMINANTS
§ 7. Euclidean Length
Appendix to § 7: Calculating with the Summation Sign
§ 8. Volumes and Determinants
Fundamental Properties of Determinants
Existence and Uniqueness of Determinants
Volumes
§ 9. The Principal Theorems of Determinant Theory
The Complete Development of a Determinant
The Determinant as a Function of its Column Vectors
The Multiplication Theorem
The Development of a Determinant by Rows or Columns
Determinants and Linear Equations
Laplace’s Expansion Theorem
§ 10. Transformation of Coordinates
General Linear Coordinate Systems
Cartesian Coordinate Systems
Continuous Deformation of a Linear Coordinate System
§ 11. Construction of Normal Orthogonal Systems and Applications
§ 12. Rigid Motions
Rigid Motions in R2
Rigid Motions in R3
§ 13. Affine Transformations
Chapter 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
Chapter IV ELEMENTS OF GROUP THEORY
§ 18. The Concept of a Group
§ 19. Subgroups; Examples
§ 20. The Basis Theorem for Abelian Groups
Chapter V LINEAR TRANSFORMATIONS AND MATRICES
§ 21. The Algebra of Linear Transformations
§ 22. Calculation with Matrices
Linear Transformations Under a Change of Coordinate System
The Determinant of a Linear Transformations
Linear Dependence of Matrices
Calculation With Matrix Polynomials
The Transpose of a Matrix
§ 23. The Minimal Polynomial; Invariant Subspaces
The Minimal Polynomial
Invariant Subspaces
The Nullspace of a Linear Transformation f(σ)
Decomposition of L into Invariant Subspaces
Geometric Interpretation
§ 24. The Diagonal Form and its Applications
Unitary Transformations
Orthogonal Transformations
Hermitian and Symmetric Matrices (Principal Axis Transformations)
§ 25. The Elementary Divisors of a Polynomial Matrix
§ 26. The Normal Form
Consequences
Linear Transformation with Prescribed Elementary Divisors
The Jordan Normal Form
Index
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Tags: Otto Schreier, Emanuel Sperner, Modern Algebra, Matrix Theory
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