Advanced linear algebra

書誌事項

Advanced linear algebra

Steven Roman

(Graduate texts in mathematics, 135)

Springer, 2008

3rd ed

  • : pbk

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注記

Includes bibliographical references (p. [507]-511) and index

内容説明・目次

内容説明

This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

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

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詳細情報

  • NII書誌ID(NCID)
    BC05041502
  • ISBN
    • 9781441924988
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    New York
  • ページ数/冊数
    xviii, 522 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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