Answer
$T$ is a linear transformation from $R^4$ into $R^4$.
Work Step by Step
Let $A$ be a $m\times n$ matrix. The function $T$, defined by $T(v)=Av$, is a linear transformation from $R^n$ into $R^m$.
Here, since $A$ is $ 4\times 4$, implies $n=m=4$.
So, $T$ is a linear transformation from $R^4$ into $R^4$.