EAN: 9783319307657

UNDERGRADUATE TEXTS IN MATHEMATICS LINEAR ALG...

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.

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