Minkowski space/3/Diagonal/Possibilities/Exercise

We equip ${}\mathbb {R} ^{3}$ with the standard-Minkowski form.

a) Give a basis of ${}\mathbb {R} ^{3}$ with the property that all diagonal entries in the Gram matrix with respect to this basis equal ${}1$.

b) Give a basis of ${}\mathbb {R} ^{3}$ with the property that all diagonal entries in the Gram matrix with respect to this basis equal ${}-1$.

c) Give a basis of ${}\mathbb {R} ^{3}$ with the property that all diagonal entries in the Gram matrix with respect to this basis equal ${}0$.

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