Is there such a thing as a condition number for a nonlinear (polynomial) matrix in multiple variables, and if so, is it something simple (I doubt it) or maybe there are multiple methods?
Equations such as:
\begin{equation} \begin{bmatrix} a_i & a_{i2} & a_{i3} & a_{i11} & b_i & b_{i3} & b_{i11} & c_i & c_{i11} & d_i\\ \end{bmatrix} \times \begin{bmatrix} x^2\\ xy \\ xz \\ x \\ y^2\\ yz \\ y \\ z^2\\ z \\ 1 \end{bmatrix} =0 \end{equation} for $i = 1,2,3$.