Advanced Linear Algebra
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ISBN-13:
9781032765723
Veröffentl:
2024
Erscheinungsdatum:
21.06.2024
Seiten:
634
Autor:
Nicholas A. Loehr
Format:
254x178x0 mm
Sprache:
Englisch
Beschreibung:
Designed for advanced undergraduate and beginning graduate students in linear of abstract algebra, Advanced Linear Algebra provides a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra in many areas of pure and applied mathematics.
1. Overview of Algebraic Systems. 2. Permutations. 3. Polynomials. 4. Basic Matrix Operations. 5. Determinants via Calculations. 6. Comparing Concrete Linear Algebra to Abstract Linear Algebra. 7. Hermitian, Positive Definite, Unitary, and Normal Matrices. 8. Jordan Canonical Forms. 9. Matrix Factorizations. 10. Iterative Algorithms in Numerical Linear Algebra. 11. Affine Geometry and Convexity. 12. Ruler and Compass Constructions. 13. Dual Vector Spaces. 14. Bilinear Forms. 15. Metric Spaces and Hilbert Spaces. 16. Finitely Generated Commutative Groups. 17. Introduction to Modules. 18. Principal Ideal Domains, Modules over PIDs, and Canonical Forms. 19. Introduction to Universal Mapping Properties. 20. Universal Mapping Problems in Multilinear Algebra
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