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Vector Spaces Over a Field

In: The Linear Algebra a Beginning Graduate Student Ought to Know

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  • Jonathan S. Golan

    (University of Haifa, Dept. of Mathematics)

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.

Suggested Citation

  • Jonathan S. Golan, 2012. "Vector Spaces Over a Field," Springer Books, in: The Linear Algebra a Beginning Graduate Student Ought to Know, edition 3, chapter 3, pages 21-38, Springer.
    • Handle: RePEc:spr:sprchp:978-94-007-2636-9_3
    DOI: 10.1007/978-94-007-2636-9_3
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