structural:summarization
Variational characterization

In the Hermitian case, eigenvalues can be given a variational characterization. The largest eigenvalue of H {\displaystyle H} is the maximum value of the quadratic form x T H x / x T x {\displaystyle \mathbf {x} ^{\textsf {T}}H\mathbf {x} /\mathbf {x} ^{\textsf {T}}\mathbf {x} }. A value of x {\displaystyle \mathbf {x} } that realizes that maximum is an eigenvector.