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One-Form


A linear real-valued function omega^1 of vectors v such that omega^1(v)|->R. Vectors (i.e., contravariant vectors or "kets" |psi>) and one-forms (i.e., covariant vectors or "bras" <phi|) are dual to each other. Therefore

 omega^1(v)=v(omega^1)=<omega^1,v>=<phi|psi>.

The operation of applying the one-form to a vector omega^1(v) is called tensor contraction.


See also

Angle Bracket, Bra, Comma Derivative, Contravariant Vector, Covariant Vector, Differential k-Form, Ket, Meromorphic One-Form, Two-Form, Vector, Zero-Form

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Cite this as:

Weisstein, Eric W. "One-Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/One-Form.html

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