1. Vector Spaces -- 2. Finite-Dimensional Vector Spaces -- 3. Linear Maps -- 4. Polynomials -- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces -- 6. Inner Product Spaces -- 7. Operators on Inner Product Spaces -- 8. Operators on Complex Vector Spaces -- 9. Operators on Real Vector Spaces -- 10. Trace and Determinant.
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
9783319110806
10.1007/978-3-319-11080-6 doi
2019757259
Algebra. Matrix theory. Linear and Multilinear Algebras, Matrix Theory.