|
|
libcats.org
Advanced Linear AlgebraJoseph RosenThis is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with important applications. For the third edition, the author has: * added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); * polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); * upgraded some proofs that were originally done only for finite-dimensional/rank cases; * added new theorems, including the spectral mapping theorem and a theorem to the effect that , dim(V) EPUB | FB2 | MOBI | TXT | RTF
* Конвертация файла может нарушить форматирование оригинала. По-возможности скачивайте файл в оригинальном формате.
Популярные книги за неделю:
Тестирование Дот Ком, или Пособие по жестокому обращению с багами в интернет-стартапахАвтор: Роман Савин
Размер книги: 5.26 Mb
Система упражнений по развитию способностей человека (Практическое пособие)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 818 Kb
Сотворение мира (3-х томник)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 817 Kb
Только что пользователи скачали эти книги:
Electron-electron interactions in disordered systemsАвтор: Efros, Автор: Pollak (ed)Категория: физика
Размер книги: 5.20 Mb
Alternative Solvents for Green ChemistryАвтор: Francesca M. KertonКатегория: Chemistry-Environmental-Material
Размер книги: 3.50 Mb
The natural history of a mountain year: four seasons in the Wasatch rangeАвтор: Claude Teancum Barnes
Размер книги: 1.14 Mb
|
|
|