Mathematics — Linear Algebra · vector-space-definition
Problem
Show that in the definition of a vector space (1.20), the additive inverse condition can be replaced with the condition that
0v=0 for all v∈V.
Here the 0 on the left side is the number 0, and the 0 on the right side is the additive identity of V.
The phrase a ``condition can be replaced'' in a definition means that the collection of objects satisfying the definition is unchanged if the original condition is replaced with the new condition.