 Secular equation (linear algebra)

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.