Numerical ranges and matrix completions
For a partial matrix \(T\) on a pattern \(\mathcal P\) let \(W_1(T)\) be its inner numerical range and \(W_2(T)\) be its outer numerical range. The authors show that \(W_1(T)=W_2(T)\) for every partial matrix \(T\) on \(\mathcal P\) if and only if a graph associated with the pattern is chordal. This extends one result of \textit{C. R. Johnson} and \textit{M. E. Lundquist} [Operator Theory: Adv. Appl. 50, 283-291 (1991; Zbl 0735.15021)] to patterns which are not necessarily reflexive and symmetric.
scientific article; zbMATH DE number 1523267