Show that a maximal invariant under g is sgnxn x1xn xn-1xn
Let X = {x ∈ Rn; all components of x are nonzero} and G be the group of transformations g(x) = (cx1, ..., cxn), c > 0. Show that a maximal invariant under G is (sgn(xn), x1/xn, ..., xn-1/xn), where sgn(x) is 1 or -1 as x is positive or negative.
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