Let $T\in\mathscr{L}(V,W)$ be a linear map and let $A$ be the matrix of $T$. We say the rank of $A$ is the dimension of the image of $T$. i.e. $$rank(A)=\dim(\text{Image}(T))$$If $rank(A)=\dim(V)\wedge\dim(W)$ then $A$ is said to be full rank.