Witt’s theorem and the isometry of lattices
O. Timothy O’Meara · Proceedings of the American Mathematical Society · 1956
February(3.4) E/-fc-a(fc)/R.Case 2. £,-improper, £y proper.Let £<±i =S<±i be the basis vector that is not orthogonal to £,.Put 2 2 2 2 2 4 = -a^-S,±i/(SiSi±i -(S.-Si+i) ) E o, B = a|i(SiSi±i)/(H,H!±i-(SÄtti) ) G o and define Sy = £y+4Si+.BSi±i; then SySi = 0=SyS,+i by choice of A and B; and (Sx) is canonical in virtue of (2.2) and (2.2a