Question: Let $(X_1,...,X_m)$ basis for $R^m$ and $(Y_1,...,Y_n)$ basis for $R^n$. Is true that the $mn$ matrices $X_iY_j^t$ forms a basis for space of all $m$ by $n$ matrices?
I verified this for standard ordered basis. But I have no idea how to proceed in general. Can some one give suggestion to this problem?
Thanks