Linear Algebra Done Right

2., nd Auflage 1997
ISBN: 978-0-387-98259-5
Verlag: Springer-Verlag New York

Buch, Englisch, 251 Seiten, GB, Format (B × H): 194 mm x 235 mm, Gewicht: 734 g

Reihe: Undergraduate Texts in Mathematics

This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Axler, Sheldon

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

1: Vector Spaces
2: Finite-Dimensional Vector Spaces
3: Linear Maps
4: Polynomials
5: Eigenvalues and Eigenvectors
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