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Tensors and differential forms

T. J. Willmore

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Abstract

Abstract In this chapter we associate new vector spaces to given vector spaces. We have already seen that corresponding to a given vector space V we have another vector space V*, namely the dual vector space consisting of linear maps of V into the field ℝ. Moreover, the reader will have met already the sum V ⊕W of two vector spaces V and W, consisting of pairs ( v, w) of V x W with the usual operations acting separately on each component.

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Abstract In this chapter we associate new vector spaces to given vector spaces. We have already seen that corresponding to a given vector space V we have another vector space V*, namely the dual vector space consisting of linear maps of V into the field ℝ. Moreover, the reader will have met already the sum V ⊕W of two vector spaces V and W, consisting of pairs ( v, w) of V x W with the usual operations acting separately on each component.

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Available abstract

Abstract In this chapter we associate new vector spaces to given vector spaces. We have already seen that corresponding to a given vector space V we have another vector space V*, namely the dual vector space consisting of linear maps of V into the field ℝ. Moreover, the reader will have met already the sum V ⊕W of two vector spaces V and W, consisting of pairs ( v, w) of V x W with the usual operations acting separately on each component.

Key concepts: Dual space, Dual pair, Vector field, Ordered vector space, Vector space, Normed vector space, Space (punctuation), Vector (molecular biology)

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