Linear Algebra: An Introduction to Abstract Mathematics

Couverture
Springer Science & Business Media, 6 déc. 2012 - 237 pages
Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.
 

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Table des matières

GROUPS AND GROUP HOMOMORPHISMS
18
VECTOR SPACES AND LINEAR TRANSFORMATIONS
37
Exercises
54
Exercises
72
Exercises
94
REPRESENTATION OF LINEAR TRANSFORMATIONS
100
Exercises
125
INNER PRODUCT SPACES
131
Exercises
147
Exercises
163
EIGENVALUES AND EIGENVECTORS
169
Exercises
181
TRIANGULATION AND DECOMPOSITION
187
SUPPLEMENTARY TOPICS
214
INDEX
233
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