The dual map of a linear transformation 
is the linear transformation
defined by
 |
It reverses direction because a linear functional on 
pulls back to one on 
. With respect to dual bases, the matrix
of 
is the transpose
of the matrix of 
.
Dual Map
See also
Dual Vector Space, Linear Functional, Linear Transformation, Pullback Map, TransposeExplore with Wolfram|Alpha
References
Lang, S. Linear Algebra, 3rd ed. New York: Springer-Verlag, 1987.Referenced on Wolfram|Alpha
Dual MapCite this as:
Weisstein, Eric W. "Dual Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DualMap.html