Beschreibung:
<jats:title>Abstract</jats:title><jats:p>We study square matrices <jats:italic>F</jats:italic>(<jats:italic>α</jats:italic>) over ℂ with <jats:italic>α</jats:italic>∈ℝ, where the eigenvalues depend on the parameter <jats:italic>α</jats:italic> but not the eigenvectors, and vice versa, where the eigenvectors depend on the parameter <jats:italic>α</jats:italic> but not the eigenvalues. We derive sufficient conditions for such properties. Applications to Lie groups and spin systems are provided. Both normal and nonnormal matrices are investigated.</jats:p>