Group of transformations, Show that a maximal invariant

Group of transformations

Reference no: EM131852074

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

Reference no: EM131852074

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