Advanced Linear Algebra

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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 module...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Roman, Steven (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2005.
Edición:2nd ed. 2005.
Colección:Graduate Texts in Mathematics, 135
Temas:
Algebras, Linear.
Linear Algebra.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Preliminaries
  • Preliminaries
  • Basic Linear Algebra
  • 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
  • Topics
  • 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.

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