The Dual Space

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

Chapter 14 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 317-332 from Springer

Abstract: Abstract Linear functionals and the dual space of a vector space are defined and characterized. Every vector space is shown to be canonically embeddable in its second dual. Maximal subspaces are characterized as kernels of nontrivial linear functionals. The trace of a square matrix is studied in detail. Over a field of characteristic 0, a square matrix is shown to have trace 0 if and only if it is the Lie product of two matrices. Taber’s theorem is established.

Keywords: Dual Space; Maximal Subspace; Linear Functionals; Nontrivial Vector Space; Baric Algebra (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_14

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DOI: 10.1007/978-94-007-2636-9_14

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