Advanced linear algebra

Steven Roman

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.

「Nielsen BookData」より

[目次]

  • Vector Spaces.- Linear Transformations.- The Isomorphism Theorems.- Modules I: Basic Properties.- Modules II: Free and Noetherian Modules.- Modules over a Principal Ideal Domain.- The Structure of a Linear Operator.- Eigenvalues and Eigenvectors.- Real and Complex Inner Product Spaces.- Structure Theory for Normal Operators.- Metric Vector Spaces: The Theory of Bilinear Forms.- Metric Spaces.- Hilbert Spaces.- Tensor Products.- Positive Solutions to Linear Systems: Convexity and Separation.- Affine Geometry.- Operator Factorizations: QR and Singular Value.- The Umbral Calculus.- References.- Index.

「Nielsen BookData」より

この本の情報

書名 Advanced linear algebra
著作者等 Roman, Steven
Roman Steven (California State University USA)
シリーズ名 Graduate texts in mathematics
出版元 Springer
刊行年月 c2005
版表示 2nd ed
ページ数 xvi, 482 p.
大きさ 24 cm
ISBN 0387247661
NCID BA71798598
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想