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
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag London Limited
About this chapter
Cite this chapter
Bapat, R.B. (2012). Vector Spaces and Subspaces. In: Linear Algebra and Linear Models. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-2739-0_1
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2739-0_1
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2738-3
Online ISBN: 978-1-4471-2739-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)