Differential properties of the numerical range map of pairs of matrices (Q1373326)

Let \(A_1\), \(A_2\) be a pair of Hermitian operators in \(\mathbb{C}^n\) and \(A= A_1+ iA_2\). The authors investigate certain differential properties of the numerical range map \(n_A: x\mapsto (\langle A_1x,x\rangle, \langle A_2x,x\rangle)\) with the aim of better understanding the nature of the numerical range \(W(A)\) of \(A\), and obtain a number of correspondences between properties of \(n_A\) and those of \(W(A)\).