
theorem Th46:
:: Schwarz inequality - second version
  for V be VectSp of F_Complex for f be diagReR+0valued
hermitan-Form of V for v,w be Vector of V holds |. f.(v,w) .|^2 <= |. f.(v,v).|
  * |. f.(w,w) .|
proof
  let V be VectSp of F_Complex, f be diagReR+0valued hermitan-Form of V, v1,w
  be Vector of V;
  set v3 = f.(v1,v1), s1 = signnorm(f,v1), s2 = signnorm(f,w);
  |. f.(v1,w) .|^2 <= s1 * s2 & s1 = |.v3.| by Th41,Th45;
  hence thesis by Th41;
end;
