Elliptic system of differential equations
= Elliptic system of differential equations
{title2=$\det A_N(\xi)\ne0\quad(\xi\ne0)$}
A square system whose entries have common maximal order $N$ is elliptic when its matrix <principal symbol> is invertible at every nonzero real frequency. Unlike scalar operators, a system can be first-order elliptic in three dimensions: the <Pauli matrices> give $A(\xi)=\sum_j\sigma_j\xi_j$ with $A(\xi)^2=|\xi|^2\mathbf1$.