R^4/Minkowski form/Orthonormal basis and orthogonal/Exercise

Suppose that ${}\mathbb {R} ^{4}$ is endowed (beside the standard inner product) with the standard Minkowski form. Give a basis of ${}\mathbb {R} ^{4}$ that is an orthonormal basis with respect to the inner product, and an orthogonal basis with respect to the Minkowski form.

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