Dimension

This chapter covers the fundamental structure theory for vector spaces. In particular, we shall show that all vector spaces admit coordinate systems (called bases) and that the number of coordinates is intrinsic to the space. These results in turn allow us to define the dimension of a vector space a...

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Bibliographic Details
Published inLinear Algebra pp. 59 - 77
Main Author Valenza, Robert J
Format Book Chapter
LanguageEnglish
Published United States Springer 1993
Springer New York
SeriesUndergraduate Texts in Mathematics
Subjects
Linear Transformation
Real Vector Space
Span Versus
Vector Space
Vector Space Versus
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Summary:This chapter covers the fundamental structure theory for vector spaces. In particular, we shall show that all vector spaces admit coordinate systems (called bases) and that the number of coordinates is intrinsic to the space. These results in turn allow us to define the dimension of a vector space and thus to recast this most basic of geometric notions in purely algebraic terms. In so doing, we extend the application of this concept to many settings that have no obvious a priori geometric interpretation.
ISBN:9781461269403
1461269407
ISSN:0172-6056
DOI:10.1007/978-1-4612-0901-0_4