AbstractGeneral properties of eigenvalues of $$A+\tau uv^*$$
A
+
τ
u
v
∗
as functions of $$\tau \in {\mathbb {C} }$$
τ
∈
C
or $$\tau \in {\mathbb {R} }$$
τ
∈
R
or $$\tau ={{\,\mathrm{{e}}\,}}^{{{\,\mathrm{{i}}\,}}\theta }$$
τ
=
e
i
θ
on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with $$\tau \rightarrow \infty $$
τ
→
∞
are discussed in detail. The following classes of matrices are considered: complex (without additional structure), real (without additional structure), complex H-selfadjoint and real J-Hamiltonian.
On normal and structured matrices under unitary structure-preserving transformations
