Dual Basis (original) (raw)

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Given a contravariant basis ${e^->_1,...,e^->_n}$ , its dual covariant basis is given by

e^->^alpha·e^->_beta=g(e^->^alpha,e^->_beta)=delta_beta^alpha,

where is the metric and delta_beta^alpha is the mixed Kronecker delta. In Euclidean space with an orthonormal basis,

e^->^j=e^->_j,

so the basis and its dual are the same.

See also

Dual Vector Space

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Cite this as:

Weisstein, Eric W. "Dual Basis." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DualBasis.html

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