Let and be two near-linear spaces.
Here, is the set . A linear function is also called a homomorphism.
If is a linear space, then so is . This shows that if is onto, is a linear space if is.
for any line in .
Suppose is an isomorphism. For every point , let be the set of all lines passing through . Then
for any point in .
It is possible to have a bijective linear function whose inverse is not linear. For example, let be the space with two points with no lines, and the space with the same two points with line . Then the identity function on is a bijective linear function whose inverse is not linear. On the other hand, if the both spaces are linear, then the inverse is always linear.
|Date of creation||2013-03-22 19:14:46|
|Last modified on||2013-03-22 19:14:46|
|Last modified by||CWoo (3771)|