One-Form (original) (raw)
TOPICS
Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology
Alphabetical Index New in MathWorld
A linear real-valued function 
of vectors 
such that 
. Vectors (i.e.,contravariant vectors or "kets"
) and one-forms (i.e., covariant vectors or "bras" 
) are dual to each other. Therefore
The operation of applying the one-form to a vector 
is called tensor contraction.
See also
Angle Bracket, Bra, Comma Derivative, Contravariant Vector, Covariant Vector, Differential_k_-Form, Ket, Vector
Explore with Wolfram|Alpha
More things to try:
Cite this as:
Weisstein, Eric W. "One-Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/One-Form.html