{disambiguate=linear algebra}
{title2=$\det(H-EI)=0$}

= Secular equation
{synonym}

The equation requiring a homogeneous matrix system for an <eigenvector> to have a nonzero solution. In an orthonormal basis, $(H-EI)c=0$ requires $\det(H-EI)=0$. For a nonorthonormal basis with overlap matrix $S$, it becomes $\det(H-ES)=0$, a <generalized eigenvalue problem>. The <nearly-free electron model> uses this condition on a resonant <plane wave> subspace.


 Secular equation (linear algebra) (source code)