Perturbation of eigenvalues in U(n) by pseudo-reflections
Dragomir Ž. Djoković, Jerry Malzan · Linear and Multilinear Algebra · 1979
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 .