Advanced Linear Algebra (Graduate Texts in Mathematics)

Springer; 3rd edition (October 8-2007) | PDF(526 pages) | 2.3mb(rar size)

Advanced Linear Algebra (Graduate Texts in Mathematics)/by Steven Roman (Author)

Description
This 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)<=dim(V*) with
equality if and only if V is finite-dimensional;
* corrected all known errors;
* the reference section has been enlarged considerably, with over a hundred references to books on linear algebra.

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