一类边界矩阵的谱

The spectrum of a class of bordered martrices

讨论了边界矩阵A=aIPTQUVT的谱问题,这里U,V,P,Q是n×k实矩阵,2k<n,a∈R,I是k×k单位矩阵.确定了矩阵A和AAT的特征多项式和特征向量,推广了Ding和Pye的结果.

This paper discusses the spectrum problem of the bordered matrix A=aIP^TQUV^T, where U,V,P,Q are n×k real matries, 2k<n,a∈R,I is the k×k identity matrix. The author determines the characteristic polynomials of A and AA^T and their eigenvectors. The results of Ding and Pye are thus extended.