Create tensor with a repeating vector starting on diagonal

Hey, I want to create a nxn tensor with a repeating vector starting on the diagonal and the rest initialized with zeros. For Example:

vector v = [v_1, v_2, v_3]

v_1,  v_2,  v_3,  0
0,    v_1,  v_2,  v_3
0,    0,    v_1,  v_2
0,    0,    0,    v_1

Is this possible? It should be, but I am currently not sure how…also can whatever the solution might be: is it possible to backprob through it?