Linear Transformations

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

Chapter 6 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 89-111 from Springer

Abstract: Abstract The notions of linear transformations, monomorphisms, epimorphisms, and isomorphisms between vector spaces and algebras over a field are introduced and studied, as are the notions of the kernel and image of a linear transformation. The rank and nullity of a linear transformation are defined and their properties are proven. The importance of the fact that the action of a linear transformation is completely determined by its values on any basis is emphasized through several examples.

Keywords: Bijective Linear Transformation; Nontrivial Vector Space; Isomorphism; Epimorphism; Bijective Homomorphism (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-94-007-2636-9_6

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