Linear Algebra : an Introduction to Abstract Mathematics
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
1 online resource (xviii, 237 pages)
9781461209010, 1461209013
853266255
Print version:
Topics covered include: Sets and functions
Groups and group homomorphisms
Vector spaces and linear transformations
Dimension
Matrices
Representation of linear transformations
Inner product spaces
Determinants
Eigenvalues and eigenvectors
Triangulation and decomposition of endomorphisms. Supplementary chapters discuss the connection between linear algebra and multivariate calculus and introduce categories and functors
English