Linear Algebra: An Introduction to Abstract Mathematics (Undergraduate Texts in Mathematics) Book

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 linear algebra texts at this level, it introduces group theory early in the discussion, both as mathematical preparation for vector spaces and as a preliminary example of the rigorous development of informal axiomatic systems. Topics covered include: sets and functions; groups and group homomorphisms; vector spaces and linear transformations; basis and dimension; matrices; representation of linear transformations; inner product spaces; determinants; eigenvectors and eigenvalues; and triangulation of endormorphisms and reduction to normal forms. A supplementary chapter discusses the connection between linear algebra and multivariate calculus and introduces categories and functors.Read More