Advanced Linear Algebra, Second Edition takes a gentle approach that starts with familiar concepts and then gradually builds to deeper results. Each section begins with an outline of previously introduced concepts and results necessary for mastering the new material. By reviewing what students need to know before moving forward, the text builds a solid foundation upon which to progress.
The new edition of this successful text focuses on vector spaces and the maps between them that preserve their structure (linear transformations). Designed for advanced undergraduate and beginning graduate students, the book discusses the structure theory of an operator, various topics on inner product spaces, and the trace and determinant functions of a linear operator. It addresses bilinear forms with a full treatment of symplectic spaces and orthogonal spaces, as well as explains the construction of tensor, symmetric, and exterior algebras.
Featuring updates and revisions throughout, Advanced Linear Algebra, Second Edition:
Contains new chapters covering sesquilinear forms, linear groups and groups of isometries, matrices, and three important applications of linear algebra
Adds sections on normed vector spaces, orthogonal spaces over perfect fields of characteristic two, and Clifford algebras
Includes several new exercises and examples, with a solutions manual available upon qualifying course adoption
The book shows students the beauty of linear algebra while preparing them for further study in mathematics.
Rezensionen / Stimmen
"This is the substantially extended second edition of a book comprising an advanced course in linear algebra ..."
-Zentralblatt MATH 1319
Praise for the First Edition:"The book is well written, and the examples are appropriate. ... Each section contains relevant problems at the end. The 'What You Need to Know' feature at the beginning of each section outlining the knowledge required to grasp the material is useful. Summing Up: Recommended."
-CHOICE, January 2011
"Pedagogically, a structural and general approach is taken, and topically, the material has been chosen in order to cover the material a beginning graduate student would be expected to know when taking a first course in group or field theory or functional analysis."
-SciTech Book News, February 2011
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Postgraduate
Illustrationen
9 s/w Abbildungen
9 Illustrations, black and white
Maße
Höhe: 229 mm
Breite: 152 mm
Gewicht
ISBN-13
978-1-032-91818-1 (9781032918181)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Bruce Cooperstein is a professor of mathematics at the University of California, Santa Cruz, USA. He was a visiting scholar at the Carnegie Foundation for the Advancement of Teaching (spring 2007) and a recipient of the Kellogg National Fellowship (1982-1985) and the Pew National Fellowship for Carnegie Scholars (1999-2000). Dr. Cooperstein has authored numerous papers in refereed mathematics journals.
Vector Spaces. Linear Transformations. Polynomials. Theory of a Single Linear Operator. Normed and Inner Product Spaces. Linear Operators on Inner Product Spaces. Trace and Determinant of a Linear Operator. Bilinear Forms. Sesquilinear Forms and Unitary Geometry. Tensor Products. Linear Groups and Groups of Isometries. Additional Topics in Linear Algebra. Applications of Linear Algebra. Appendices.
