There's a question that asks me to show that there exists a unique linear transformation from: [tex]f\otimes g: V_1\otimes W_1\rightarrow V_2\otimes W_2[/tex] where f and g are linear transformations f:V1->V2, g:W1->W2 that satisfies: [tex](f\otimes g)(u\otimes v)=f(u)\otimes g(v)[/tex] well I think that what I need to show is only that it's linear by first componenet and second componenet which I did. well if that's it for linear (including multplication by a scalar), then now I need to show uniqueness, well I guess this depends on f and g is it not? well it's unique by our choice of f and g, with other functions we would have a different linear transformation. What do I miss here? thanks in advance.