Ebook: A Second Course in Linear Algebra

This textbook for senior undergraduate and first year graduate-level courses in linear algebra and analysis, covers linear algebra, multilinear algebra, canonical forms of matrices, normal linear vector spaces and inner product spaces. These topics provide all of the prerequisites for graduate students in mathematics to prepare for advanced-level work in such areas as algebra, analysis, topology and applied mathematics.
Presents a formal approach to advanced topics in linear algebra, the mathematics being presented primarily by means of theorems and proofs. Covers multilinear algebra, including tensor products and their functorial properties. Discusses minimal and characteristic polynomials, eigenvalues and eigenvectors, canonical forms of matrices, including the Jordan, real Jordan, and rational canonical forms. Covers normed linear vector spaces, including Banach spaces. Discusses product spaces, covering real inner product spaces, self-adjoint transformations, complex inner product spaces, and normal operators.