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Vector Spaces and Subspaces

  • R. B. Bapat
Chapter
  • 5.9k Downloads
Part of the Universitext book series (UTX)

Abstract

Preliminaries concerning matrices and matrix operations are reviewed. Properties of determinant are recalled without proof. Vector spaces, linear independence, basis and dimension are introduced. It is shown that any two bases of a vector space have the same cardinality and that two vector spaces are isomorphic if and only if they have the same dimension. Extension of a linearly independent set to a basis is considered.

Keywords

Vector Space Subspace Linear Independence Zero Vector Determinant Changes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • R. B. Bapat
    • 1
  1. 1.Indian Statistical InstituteNew DelhiIndia

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