Linear Independence and Dimension

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

Chapter 5 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 57-88 from Springer

Abstract: 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.

Keywords: Linear Independence; Hausdorff Maximal Principle; Arbitrary Vector Space; Linear Dependent Set; Partially-ordered Set (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-94-007-2636-9_5

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