A left inverse of a function 
between sets 
and 
is a function 
satisfying 
, so composing 
with 
from the left gives the identity
function on 
. Often 
is a function of a specific type,
such as a linear transformation between
vector spaces or a continuous
function between topological spaces. In
each such case, a left inverse is often required to be of the same type as 
.
Left Inverse
See also
Inverse, Right InversePortions of this entry contributed by Rasmus Hedegaard
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References
Lee, J. M. Introduction to Topological Manifolds. New York: Springer, 2000.Mac Lane, S. and Birkhoff, G. §1.2 in Algebra, 3rd ed. Providence, RI: Amer. Math. Soc., 1999.Referenced on Wolfram|Alpha
Left InverseCite this as:
Weisstein, Eric W., with contributions by Rasmus Hedegaard. "Left Inverse." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LeftInverse.html