Editing Hessenberg matrix (section)

==Hessenberg operator==
The Hessenberg operator is an infinite dimensional Hessenberg matrix. It commonly occurs as the generalization of the [[Jacobi operator]] to a system of [[orthogonal polynomials]] for the space of [[square-integrable]] [[holomorphic functions]] over some domain—that is, a [[Bergman space]]. In this case, the Hessenberg operator is  the right-[[shift operator]] <math>S</math>, given by 
<math display="block">[Sf](z) = z f(z).</math>

The [[eigenvalue]]s of each principal submatrix of the Hessenberg operator are given by the [[characteristic polynomial]] for that submatrix. These polynomials are called the [[Bergman polynomial]]s, and provide an [[orthogonal polynomials|orthogonal polynomial]] basis for Bergman space.