# Perturbation of eigenvalues in U(n) by pseudo-reflections

@inproceedings{Djokovi1979PerturbationOE, title={Perturbation of eigenvalues in U(n) by pseudo-reflections}, author={Dragomir Z. Djokovi{\'c} and Jerry Malzan}, year={1979} }

- Published 1979
DOI:10.1080/03081087908817297

A unitary pseudo-reflection is a matrix where a is a unit vector in Cn . If is a unitary matrix we study the variation of eigenvalues of ARθ when θ increases from 0 to 2π. Some of these eigenvalues may remain fixed while the others move monotonicaliy and counter-clockwise along the unit circle. As a byproduct, we obtain an explicit formula for the determinant of the matrix whose (i,j)th entry is .