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A degree ''n'' form itself is a covariant of degree ''n'' and order 1.
The Hessian covariant of a form {{harvtxt|Hilbert|1993|loc=p.88}} is the determinant of the [[Hessian matrix]]
:<math>
\frac{\partial^2 f}{\partial x^2} & \frac{\partial^2 f}{\partial x\,\partial y} \\
\frac{\partial^2 f}{\partial y\,\partial x} & \frac{\partial^2 f}{\partial y^2} \\
\end{bmatrix}.</math>
It is a covariant of degree 2''n''− 4 and order 2.
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