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6
votes
Thread map to 2 lists of inputs, including the nondiagonal terms
a = {a1, a2, a3};
b = {b1, b2, b3};
f @@@ Tuples[{a, b}]
(* {f[a1, b1], f[a1, b2], f[a1, b3],
f[a2, b1], f[a2, b2], f[a2, b3],
f[a3, b1], f[a3, b2], f[a3, b3]} *)