Given a map 
between sets 
and 
, the map 
is called a left inverse to 
provided that 
, that is, composing 
with 
from the left gives the identity on 
. Often 
is a map of a specific type, such as a linear map between
vector spaces, or a continuous map between topological spaces, and in each such case,
one often requires a right inverse to be of the same type as that of 
.
Left Inverse
See also
Inverse, Right InverseThis 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:
Hedegaard, Rasmus. "Left Inverse." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LeftInverse.html