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    Graduate How to find a basis of a subspace V = {(x1; x2;….; xn) | Σni=1 xi=0}

    Given V = {(x1; x2;….; xn) | Σni=1 xi=0} (sum of vectors is equal to zero) be a subspace of Rn. How can we find a basis of V such that for each vector {(x1; x2;….; xn) in the basis Σi=1n x2i=1 ( i.e. sum of squares is equal to 1).