Linear Algebra

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. TOC: Topics covered include: Sets and functions.- Groups and group homomorphisms.- Vector spaces and linear transformations.Dimension.- Matrices.- Representations of linear transformations.- Inner product spaces.- Determinants.- Eigenvalues and eigenvectors.- Triangulation and decompsition of endomorphisms. Supplementary chapters discuss the connection between linear algebra and multivariate calculus and introduce categories and functors.