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.
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© 2012 Springer-Verlag London Limited
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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
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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
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