Normed Division Algebra - Hurwitz's Theorem

Hurwitz's Theorem

Hurwitz's theorem (also called the "1,2,4 8 Theorem"), named after Adolf Hurwitz, who proved it in 1898, shows that the product of the sum of n squares by the sum of n squares is the sum of n squares in a bilinear way only when n is equal to 1, 2, 4 or 8. The original proof is for quadratic forms with coefficients taken in C but extends to any field of characteristic not 2.