André Lukas
Abstract
Abstract The dual vector space associated to a vector space is defined. The dual basis is introduced and it is shown that a vector space and its dual have the same dimension. The double turns our to be canonically isomorphic to the original vector space. We discuss the dual map which is an abstract version of matrix transposition.
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Abstract The dual vector space associated to a vector space is defined. The dual basis is introduced and it is shown that a vector space and its dual have the same dimension. The double turns our to be canonically isomorphic to the original vector space. We discuss the dual map which is an abstract version of matrix transposition.
Key concepts: Dual space, Dual pair, Ordered vector space, Dual (grammatical number), Normed vector space, Space (punctuation), Dimension (graph theory), Vector space