vector spaces – Generalization of this property of Lorentz Group

From this PhySE Post we can conclude that for any two set
$$p=(p^0,p^1,p^2,p^3),k=(k^0,k^1,k^2,k^3) in mathbb{R}^4$$
if their Minkowski Norm is same:
$$(p^1)^2+(p^2)^2+(p^3)^2-(p^0)^2 = (k^1)^2+(k^2)^2+(k^3)^2-(k^0)^2 $$

(And for negative norm,$p^0k^0>0$), then there exists a linear transformation $Lambda:mathbb{R}^4tomathbb{R}^4$ which preserves Minkowski Norm for all $xin mathbb{R}^4$ and
$$p = Lambda k $$

My question is whether there is a generalization of this result for arbitrary Vector space with an inner-product which is not necessarily non-negative.