Given a map $f:\mathbb{R}^m\rightarrow \mathbb{R}^n$, is the condition that for all $x,y$ in $\mathbb{R}^m$, $f(x+y)=f(x)+f(y)$ enough for $f$ to be $\mathbb{R}$-linear? I cannot prove it or think of a counter example.
Asked
Active
Viewed 58 times
0
-
2this question should give you an answer for the case where $m=n=1$ – Mor A. Oct 13 '20 at 08:34
