Abstract
The notions of linear independence and bases are defined and studied for arbitrary vector spaces. The notion of dimension is defined. To study bases for arbitrary vector spaces, the Hausdorff Maximum Principle is introduced and used. The properties of finite-dimensional vector spaces are considered. Finally, independence and complements in the lattice of subspaces of a vector space are studied. Among the examples given are the quaternion algebras, Hamel bases, and the complexification of real vector spaces.
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© 2012 Springer Science+Business Media B.V.
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Golan, J.S. (2012). Linear Independence and Dimension. In: The Linear Algebra a Beginning Graduate Student Ought to Know. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2636-9_5
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DOI: https://doi.org/10.1007/978-94-007-2636-9_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2635-2
Online ISBN: 978-94-007-2636-9
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