A Some Concepts in Linear Algebra In the interest of self-containedness, we provide a brief review of some concepts from linear algebra

Addition and scalar multiplication are defined in the obvious way by pa,b q ` λ pc,d q: " p a ` λc,b ` λd q for a,c P H, b,d P p H and λ P C . 'size' by what is called the operator norm, denoted by } } We may then write f " In this case we write R pz, q " p z q It is a standard exercise to show that this is independent of the choice of orthonormal basis. To streamline the argumentation let us first introduce some notation: 18 Notation C.2. Lemma A.1), we find a To investigate the example of Figure 3, we label the vertices of the respective graphs as depicted in Figure 6. Such operators are positive and hence | | " (similarly for r). " 0. Next we note }Jf } " J and determine Ă J It remains to establish (9).