1993 | OriginalPaper | Buchkapitel
Dimension
verfasst von : Robert J. Valenza
Erschienen in: Linear Algebra
Verlag: Springer New York
Enthalten in: Professional Book Archive
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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.