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.