Abstract
In this chapter, abstract vector spaces and their subspaces are introduced and their elementary properties are established. Elementary properties of the lattice of subspaces of a vector space, such as the Modular Law, are proven. Direct products and coproducts are used to construct new spaces from given ones. Generating sets for vector spaces are defined and studied, and the notion of a finitely-generated space is introduced.
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Notes
- 1.
Triangular norms play a very important part in the theory of probabilistic metric spaces and have important applications in statistics and in mathematical economics, as well as such areas as pattern recognition and capacity theory.
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© 2012 Springer Science+Business Media B.V.
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Golan, J.S. (2012). Vector Spaces Over a Field. In: The Linear Algebra a Beginning Graduate Student Ought to Know. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2636-9_3
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DOI: https://doi.org/10.1007/978-94-007-2636-9_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2635-2
Online ISBN: 978-94-007-2636-9
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