Complete the square to determine the signature of the following quadratic forms:
a) [tex]h(x,y) = xy[/tex]
b) [tex]h(x,y,z) = yz[/tex]
c) [tex]h(x,y,z) = x^2 + y^2 + z^2 + 2xy + 2xz + yz[/tex]
The Attempt at a Solution
I suspect there's a really simple trick to this, but I can't seem to figure it out at the moment.
For c), we get [tex]h(x,y,z) = x^2 + 2xy + 2xz + y^2 + yz + z^2 = x^2 + 2x(y+z) + y^2 + yz + z^2 = (x+y+z)^2 - (y+z)^2 + y^2 + yz + z^2 = (x+y+z)^2 - yz[/tex], but I suspect that would require a solution of b) to get further.