Vector Spaces Over a Field

Jonathan S. Golan ()
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Jonathan S. Golan: University of Haifa, Dept. of Mathematics

Chapter 3 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 21-38 from Springer

Abstract: 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.

Keywords: Vector Space; Nonempty Subset; Identity Element; Scalar Multiplication; Vector Space Versus (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-007-2636-9_3

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DOI: 10.1007/978-94-007-2636-9_3

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