Eigenvalues of Bordered Matrix
Tang Gao-hua · Journal of Guangxi Teachers Education University · 2006
Ba is called a bordered matrix of A if A is a Hermite matrix with order n,β is a n-dimensional complex vector and a is a real number.Suppose that the eigenvalues of A and B are λ_1≥λ_2≥…≥λ_n and μ_1≥μ_2≥…≥μ_(n+1) respectively.It was proved in the document by WANG Song-gui,et al.that μ_1≥λ_1≥μ_2≥…≥λ_(n-1)≥μ_n≥λ_n≥μ_(n+1).In this paper,we give a new proof of this result by using properties of contiguous function.