Advanced Linear Algebra (Graduate Texts in Mathematics)
by Steven Roman (Author)
Hardcover: 504 pages
Publisher: Springer; 2nd ed. edition (March 22, 2005)
Language: English
Review
From the reviews of the first edition:
" The book is very well written and has a good set of exercises. It is a suitable choice as a graduate textbook as well as a reference book." A.A. Jafarian for ZentralblattMATH
From the reviews of the second edition:
"In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials. As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields. the exercises are rewritten and expanded. Overall, I found the book a very useful one. It is a suitable choice as a graduate text or as a reference book." (Ali-Akbar Jafarian, Zentralblatt MATH, Vol. 1085, 2006)
"This is a formidable volume, a compendium of linear algebra theory, classical and modern . The development of the subject is elegant . The proofs are neat . The exercise sets are good, with occasional hints given for the solution of trickier problems. It represents linear algebra and does so comprehensively." (Henry Ricardo, MathDL, May, 2005)
Book 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.
The second edition contains two new chapters: a chapter on convexity, separation and positive solutions to linear systems and a chapter on the QR decomposition, singular values and pseudoinverses. The treatments of tensor products and the umbral calculus have been greatly expanded and there is now a discussion of determinants (in the chapter on tensor products), the complexification of a real vector space, Schur's lemma and Gersgorin disks.
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