If $Q$ is a quadratic form, then we know there exists matrix $A$ such that $Q=xAx'$ and $Q$ can be expressed as weighted sum of eigenvalues of $A$.
If $H$ is a higher order form, then is there an object $B$(like tensors) that can be used to encode $H$ and are their analogous objects to eigenvalues that $H$ can be represented with?
Please provide concrete examples. And also available references?