Math 6310 • Algebra

\begin{enumerate}
\item
Determine the rank and signature of the real quadratic form
\[
x_1x_2+x_2x_3+x_3x_4+x_4x_1.
\]
(There are different definitions of signature, so state the one you use!)

\item
Up to isometry, what is the number of distinct quadratic forms on \(\mathbb{R}^4\)?
\end{enumerate}