\hint{\ref{ex:SameD}}{
On a vector in the domain of one but not the other, take an outrageous
value for $U$, that will raise or lower the signature.
}
\hint{\ref{ex:SameQ}}{
WLOG, $Q_1$ is diagonal and $Q_1=0$.
}
\hint{\ref{ex:PushOfPull}}{
It's enough to test that against $U$ with $\calD(U)=\im\phi$.
}
\hint{\ref{ex:Uzero}}{
The ``shift'' part of $0_*S$ is $\sigma(S)$.
}
\hint{\ref{ex:Szero}}{
$\phi_*S$ isn't $0$, it's the {\em partial} quadratic ``$0$ on
$\im\phi$'' (and indeed, $\sigma(\phi^*U)=\sigma(U)$ if $\phi$ is surjective).
}
\hint{\ref{ex:Eleven}}{
The exceptions are ${01}\atop{00}$, ${00}\atop{10}$, ${01}\atop{11}$, and ${11}\atop{10}$.
}
\hint{\ref{ex:sums}}{
Use Exercise~\ref{ex:iff}.
}
