Nicholas A Loehr

Advanced Linear Algebra

• Gebundenes Buch

Produktbeschreibung

Designed for a second theoretical course in linear algebra, this text explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The author covers algebraic structures, matrices, structured matrices, geometric aspects of linear algebra, modules, and multilinear algebra. He gives complete proofs of all results and supplements the general theory with many specific examples and concrete computations.

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Produktdetails

• Verlag: Taylor & Francis Ltd (Sales)
• Seitenzahl: 632
• Erscheinungstermin: 10. April 2014
• Englisch
• Abmessung: 261mm x 184mm x 38mm
• Gewicht: 1230g
• ISBN-13: 9781466559011
• ISBN-10: 1466559012
• Artikelnr.: 40038869

Autorenporträt

Nicholas Loehr

Inhaltsangabe

Background on Algebraic Structures. Overview of Algebraic Systems.
Permutations. Polynomials. Matrices. Basic Matrix Operations. Determinants
via Calculations. Concrete vs. Abstract Linear Algebra. Matrices with
Special Structure. Hermitian, Positive Definite, Unitary, and Normal
Matrices. Jordan Canonical Forms. Matrix Factorizations. Iterative
Algorithms in Numerical Linear Algebra. The Interplay of Geometry and
Linear Algebra. Affine Geometry and Convexity. Ruler and Compass
Constructions. Dual Spaces and Bilinear Forms. Metric Spaces and Hilbert
Spaces. Modules, Independence, and Classification Theorems. Finitely
Generated Commutative Groups. Axiomatic Approach to Independence, Bases,
and Dimension. Elements of Module Theory. Principal Ideal Domains, Modules
over PID's, and Canonical Forms. Universal Mapping Properties and
Multilinear Algebra. Introduction to Universal Mapping Properties.
Universal Mapping Problems in Multilinear Algebra. Appendix: Basic
Definitions. Sets. Functions. Relations. Partially Ordered Sets. Further
Reading. Bibliography. Index.