The Joint Numerical Range of Bordered and Tridiagonal Matrices
Μαρία Αδάμ, John Maroulas · Birkhäuser Basel eBooks · 2002
Let Am (m = 1, …, k) be n × n matrices, the joint numerical range is defined by $$JNR[{A_1}, \ldots ,{A_k}] = \left\{ {\left( {{x^*}{A_1}x, \ldots ,{A_k}x} \right):x \in {C^n},\parallel x\parallel = 1} \right\}.$$ In this paper, some geometric properties of JNR are presented, when the hermitian Am are bordered or (2μ–C1)–Cdiagonal matrices and the convexity of JNR is investigated.