Why would a left inverse be different from a right inverse?
2.
A function with a left inverse is necessarily injective.
3.
A "'split epimorphism "'is an homomorphism that has a left inverse.
4.
If the operation * is associative then if an element has both a left inverse and a right inverse, they are equal.
5.
In classical mathematics, every injective function with a nonempty domain necessarily has a left inverse; however, this may fail in constructive mathematics.
6.
I don't know how to use only " that " to establish that the coefficient matrix of an underdetermined system has no left inverse.
7.
For instance, a left inverse of the inclusion of the two-element set in the reals violates indecomposability by giving a retraction of the real line to the set.
8.
The notions of "'right or left quasiregularity "'correspond to the situations where 1 & minus; " r " has a right or left inverse, respectively.
9.
However, if is a left inverse for, then may or may not be a right inverse for; and if is a right inverse for, then is not necessarily a left inverse for.
10.
However, if is a left inverse for, then may or may not be a right inverse for; and if is a right inverse for, then is not necessarily a left inverse for.
