Linear Algebra: An Introduction to Abstract Mathematics

Description

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. Front Matter....Pages i-xviii Sets and Functions....Pages 1-17 Groups and Group Homomorphisms....Pages 18-36 Vector Spaces and Linear Transformations....Pages 37-58 Dimension....Pages 59-77 Matrices....Pages 78-99 Representation of Linear Transformations....Pages 100-130 Inner Product Spaces....Pages 131-150 Determinants....Pages 151-168 Eigenvalues and Eigenvectors....Pages 169-186 Triangulation and Decomposition of Endomorphisms....Pages 187-213 Back Matter....Pages 214-237